Journal of the London Mathematical Society-Second Series最新文献

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Solvability and uniqueness of solution of generalized ★ $star$ -Sylvester equations with arbitrary coefficients
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-18 DOI: 10.1112/jlms.70129
Fernando De Terán, Bruno Iannazzo
{"title":"Solvability and uniqueness of solution of generalized \u0000 \u0000 ★\u0000 $star$\u0000 -Sylvester equations with arbitrary coefficients","authors":"Fernando De Terán, Bruno Iannazzo","doi":"10.1112/jlms.70129","DOIUrl":"https://doi.org/10.1112/jlms.70129","url":null,"abstract":"<p>We analyze the consistency and uniqueness of solution of the generalized <span></span><math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math>-Sylvester equation <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>X</mi>\u0000 <mi>B</mi>\u0000 <mo>+</mo>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>X</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 <mi>D</mi>\u0000 <mo>=</mo>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 <annotation>$AXB+CX^star D=E$</annotation>\u0000 </semantics></math>, with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>,</mo>\u0000 <mi>B</mi>\u0000 <mo>,</mo>\u0000 <mi>C</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$A,B,C, D$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> being complex matrices (and <span></span><math>\u0000 <semantics>\u0000 <mi>★</mi>\u0000 <annotation>$star$</annotation>\u0000 </semantics></math> being either the transpose or the conjugate transpose). In particular, we obtain characterizations for the equation to have at most one solution and to be consistent for any right-hand side. Such characterizations are given in terms of spectral properties of the matrix pencils <span></span><math>\u0000 <semantics>\u0000 <mfenced>\u0000 <mtable>\u0000 <mtr>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mtd>\u0000 <mtd>\u0000 <msup>\u0000 <mi>B</mi>\u0000 <mi>★</mi>\u0000 </msup>\u0000 </mtd>\u0000 </mtr>\u0000 <mtr>\u0000 <mtd>\u0000 <mi>A</mi>\u0000 </mtd>\u0000 <mtd>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 </mtd>\u0000 </mtr>\u0000 </mtable>\u0000 </mfenced>\u0000 <annotation>$left[begin{smallmatrix}lambda D^star & B^star A & lambda Cend{smallmatrix}right]$</annota","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shift orbits for elementary representations of Kronecker quivers
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70122
Daniel Bissinger
{"title":"Shift orbits for elementary representations of Kronecker quivers","authors":"Daniel Bissinger","doi":"10.1112/jlms.70122","DOIUrl":"https://doi.org/10.1112/jlms.70122","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mrow>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$r in mathbb {N}_{geqslant 3}$</annotation>\u0000 </semantics></math>. We denote by <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <annotation>$K_r$</annotation>\u0000 </semantics></math> the wild <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math>-Kronecker quiver with <span></span><math>\u0000 <semantics>\u0000 <mi>r</mi>\u0000 <annotation>$r$</annotation>\u0000 </semantics></math> arrows <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>γ</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <mn>1</mn>\u0000 <mo>⟶</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$gamma _i colon 1 longrightarrow 2$</annotation>\u0000 </semantics></math> and consider the action of the group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>G</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <mo>⊆</mo>\u0000 <mo>Aut</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$G_r subseteq operatorname{Aut}(mathbb {Z}^2)$</annotation>\u0000 </semantics></math> generated by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mo>:</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>⟶</mo>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variational stabilization of degenerate p $p$ -elasticae
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70096
Tatsuya Miura, Kensuke Yoshizawa
{"title":"Variational stabilization of degenerate \u0000 \u0000 p\u0000 $p$\u0000 -elasticae","authors":"Tatsuya Miura,&nbsp;Kensuke Yoshizawa","doi":"10.1112/jlms.70096","DOIUrl":"https://doi.org/10.1112/jlms.70096","url":null,"abstract":"<p>A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-elasticae. It was known that in the nondegenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$pin (1,2]$</annotation>\u0000 </semantics></math>, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$pin (2,infty)$</annotation>\u0000 </semantics></math> there emerge uncountably many local minimizers with diverging energy.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Size-Ramsey numbers of graphs with maximum degree three
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70116
Nemanja Draganić, Kalina Petrova
{"title":"Size-Ramsey numbers of graphs with maximum degree three","authors":"Nemanja Draganić,&nbsp;Kalina Petrova","doi":"10.1112/jlms.70116","DOIUrl":"https://doi.org/10.1112/jlms.70116","url":null,"abstract":"&lt;p&gt;The size-Ramsey number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$hat{r}(H)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the smallest number of edges a (host) graph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can have, such that for any red/blue colouring of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, there is a monochromatic copy of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;annotation&gt;$G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Recently, Conlon, Nenadov and Trujić showed that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a graph on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;annotation&gt;$n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; vertices and maximum degree three, then &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;8&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$hat{r}(H) = O(n^{8/5})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, improving upon the upper bound of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70116","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ergodic averages along sequences of slow growth
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-11 DOI: 10.1112/jlms.70124
Kaitlyn Loyd, Sovanlal Mondal
{"title":"Ergodic averages along sequences of slow growth","authors":"Kaitlyn Loyd,&nbsp;Sovanlal Mondal","doi":"10.1112/jlms.70124","DOIUrl":"https://doi.org/10.1112/jlms.70124","url":null,"abstract":"<p>We consider pointwise almost everywhere convergence of weighted ergodic averages along the sequence <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math> denotes the number of prime factors of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$ n$</annotation>\u0000 </semantics></math> counted with multiplicities. It was previously shown that a pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math> functions does not hold along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. We classify the strength of this divergence by proving a double-logarithmic pointwise ergodic theorem for <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> functions along <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ Omega (n)$</annotation>\u0000 </semantics></math>. This contrasts the behavior of Khintchine-type averages, for which, under any weaker form of averaging, there exists a bounded measurable function for which almost everywhere convergence fails. Moreover, we show that certain perturbations of increasing subpolynomial sequences fail to satisfy a pointwise ergodic theorem, yielding natural new examples of such sequences.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70124","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Einstein metrics on aligned homogeneous spaces with two factors
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-10 DOI: 10.1112/jlms.70120
Jorge Lauret, Cynthia Will
{"title":"Einstein metrics on aligned homogeneous spaces with two factors","authors":"Jorge Lauret,&nbsp;Cynthia Will","doi":"10.1112/jlms.70120","DOIUrl":"https://doi.org/10.1112/jlms.70120","url":null,"abstract":"&lt;p&gt;Given two homogeneous spaces of the form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_1/K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_2/K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are compact simple Lie groups, we study the existence problem for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_1times G_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-invariant Einstein metrics on the homogeneous space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$M=G_1times G_2/K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. For the large subclass &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {C}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of spaces having three pairwise inequivalent isotropy irreducible summands (12 infinite families and 70 sporadic examples), we obtain that existence is equivalent to the existence of a real root for certain quartic polynomial depending on the dimensions and two Killing constants, which allows a full classification and the possibility to weigh the existence and nonexistence pieces of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {C}$&lt;/annotation&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rigidity of quantum algebras
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-08 DOI: 10.1112/jlms.70118
Akaki Tikaradze
{"title":"Rigidity of quantum algebras","authors":"Akaki Tikaradze","doi":"10.1112/jlms.70118","DOIUrl":"https://doi.org/10.1112/jlms.70118","url":null,"abstract":"<p>Given an associative <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>-algebra <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, we call <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> strongly rigid if for any pair of finite subgroups of its automorphism groups <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>$G, H$</annotation>\u0000 </semantics></math>, such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>G</mi>\u0000 </msup>\u0000 <mo>≅</mo>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mi>H</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$A^Gcong A^H$</annotation>\u0000 </semantics></math>, then <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid. We also solve the inverse Galois problem for a wide class of rational Cherednik algebras that includes all (simple) classical generalized Weyl algebras, and also for quantum tori. Finally, we show that the Picard group of an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-dimensional quantum torus is isomorphic to the group of its outer automorphisms.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70118","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher order Lipschitz Sandwich theorems
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-07 DOI: 10.1112/jlms.70121
Terry Lyons, Andrew D. McLeod
{"title":"Higher order Lipschitz Sandwich theorems","authors":"Terry Lyons,&nbsp;Andrew D. McLeod","doi":"10.1112/jlms.70121","DOIUrl":"https://doi.org/10.1112/jlms.70121","url":null,"abstract":"&lt;p&gt;We investigate the consequence of two &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Lip&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathrm{Lip}}(gamma)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; functions, in the sense of Stein, being close throughout a subset of their domain. A particular consequence of our results is the following. Given &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$K_0 &gt; varepsilon &gt; 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mi&gt;η&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$gamma &gt; eta &gt; 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, there is a constant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;η&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$delta = delta (gamma,eta,varepsilon,K_0) &gt; 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for which the following is true. Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;mo&gt;⊂&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Sigma subset {mathbb {R}}^d$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be closed and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$f, h: Sigma rightarrow {mathbb {R}}$&lt;/annotation&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70121","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143571227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-07 DOI: 10.1112/jlms.70119
Félicien Comtat, Jolanta Marzec-Ballesteros, Abhishek Saha
{"title":"Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2","authors":"Félicien Comtat,&nbsp;Jolanta Marzec-Ballesteros,&nbsp;Abhishek Saha","doi":"10.1112/jlms.70119","DOIUrl":"https://doi.org/10.1112/jlms.70119","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$L^2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-normalized Siegel cusp form for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Sp&lt;/mi&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Sp}_4({mathbb {Z}})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of weight &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; that is a Hecke eigenform and not a Saito–Kurokawa lift. Assuming the generalized Riemann hypothesis, we prove that its Fourier coefficients satisfy the bound &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mo&gt;≪&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Γ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70119","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143564936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Substitutions on compact alphabets
IF 1 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-03-06 DOI: 10.1112/jlms.70123
Neil Mañibo, Dan Rust, James J. Walton
{"title":"Substitutions on compact alphabets","authors":"Neil Mañibo,&nbsp;Dan Rust,&nbsp;James J. Walton","doi":"10.1112/jlms.70123","DOIUrl":"https://doi.org/10.1112/jlms.70123","url":null,"abstract":"<p>We develop a systematic approach to continuous substitutions on compact Hausdorff alphabets. Focussing on implications of irreducibility and primitivity, we highlight important features of the topological dynamics of their (generalised) subshifts. We then reframe questions from ergodic theory in terms of spectral properties of a corresponding substitution operator. This requires an extension of standard Perron–Frobenius theory to the setting of Banach lattices. As an application, we identify computable criteria that guarantee quasi-compactness of the substitution operator. This allows unique ergodicity to be verified for several classes of examples. For instance, it follows that every primitive and constant length substitution on an alphabet with an isolated point is uniquely ergodic, a result which fails when there are no isolated points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70123","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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