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

{"title":"A stable splitting of factorisation homology of generalised surfaces","authors":"Florian Kranhold","doi":"10.1112/jlms.70089","DOIUrl":"https://doi.org/10.1112/jlms.70089","url":null,"abstract":"<p>For a manifold <span></span><math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$W$</annotation>\u0000 </semantics></math> and an <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mi>d</mi>\u0000 </msub>\u0000 <annotation>$smash{E_{smash{d}} }$</annotation>\u0000 </semantics></math>-algebra <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, the factorisation homology <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mo>∫</mo>\u0000 <mi>W</mi>\u0000 </msub>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$smash{int _W A}$</annotation>\u0000 </semantics></math> can be seen as a generalisation of the classical configuration space of labelled particles in <span></span><math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$W$</annotation>\u0000 </semantics></math>. It carries an action by the diffeomorphism group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Diff</mi>\u0000 <msub>\u0000 <mrow></mrow>\u0000 <mi>∂</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>W</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{Diff}{}_partial (W)$</annotation>\u0000 </semantics></math>, and for the generalised surfaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>≔</mo>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mo>#</mo>\u0000 <mi>g</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∖</mo>\u0000 <msup>\u0000 <mover>\u0000 <mi>D</mi>\u0000 <mo>˚</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70089","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431504","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}

{"title":"Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibres","authors":"Lukas Bertsch,&nbsp;Ádám Gyenge,&nbsp;Balázs Szendrői","doi":"10.1112/jlms.70074","DOIUrl":"https://doi.org/10.1112/jlms.70074","url":null,"abstract":"<p>We prove a universal substitution formula that compares generating series of Euler characteristics of Nakajima quiver varieties associated with affine ADE diagrams at generic and at certain non-generic stability conditions via a study of collapsing fibres in the associated variation of GIT map, unifying and generalising earlier results of the last two authors with Némethi and of Nakajima. As a special case, we compute generating series of Euler characteristics of non-commutative Quot schemes of Kleinian orbifolds. In type A and rank 1, we give a second, combinatorial proof of our substitution formula, using torus localisation and partition enumeration. This gives a combinatorial model of the fibres of the variation of GIT map, and also leads to relations between our results and the representation theory of the affine and finite Lie algebras in type A.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431438","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}

{"title":"On the real-rootedness of the Eulerian transformation","authors":"Christos A. Athanasiadis","doi":"10.1112/jlms.70083","DOIUrl":"https://doi.org/10.1112/jlms.70083","url":null,"abstract":"<p>The Eulerian transformation is the linear operator on polynomials in one variable with real coefficients that maps the powers of this variable to the corresponding Eulerian polynomials. The derangement transformation is defined similarly. Brändén and Jochemko have conjectured that the Eulerian transforms of a class of polynomials with nonnegative coefficients, which includes those having all their roots in the interval <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$[-1,0]$</annotation>\u0000 </semantics></math>, have only real zeros. This conjecture is proven in this paper. More general transformations are introduced in the combinatorial-geometric context of uniform triangulations of simplicial complexes, where Eulerian and derangement transformations arise in the special case of barycentric subdivision, and are shown to have strong unimodality and gamma-positivity properties. General real-rootedness conjectures for these transformations, which unify various results and conjectures in the literature, are also proposed.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70083","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431437","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}

{"title":"Criteria for extension of commutativity to fractional iterates of holomorphic self-maps in the unit disc","authors":"Manuel D. Contreras,&nbsp;Santiago Díaz-Madrigal,&nbsp;Pavel Gumenyuk","doi":"10.1112/jlms.70077","DOIUrl":"https://doi.org/10.1112/jlms.70077","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a univalent non-elliptic self-map of the unit disc &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(psi _{t})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a continuous one-parameter semigroup of holomorphic functions in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &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;ψ&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;id&lt;/mi&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$psi _{1}ne {sf id}_mathbb {D}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; commutes with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This assumption does not imply that all elements of the semigroup &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(psi _t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; commute with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;annotation&gt;$varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we provide a number of sufficient conditions that guarantee that &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;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mo&gt;∘&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${psi _t circ varphi =varphi circ psi _t}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for all &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;se","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431503","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}

{"title":"Action of \u0000 \u0000 W\u0000 $W$\u0000 -type operators on Schur functions and Schur Q-functions","authors":"Xiaobo Liu,&nbsp;Chenglang Yang","doi":"10.1112/jlms.70080","DOIUrl":"https://doi.org/10.1112/jlms.70080","url":null,"abstract":"<p>In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau-functions of higher KdV hierarchies that satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov–Morozov's formula, which express the Brézin–Gross–Witten and Kontsevich–Witten tau-functions as linear combinations of Q-functions with simple coefficients, respectively.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404515","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}

{"title":"Galilean symmetry of the KdV hierarchy","authors":"Jianghao Xu,&nbsp;Di Yang","doi":"10.1112/jlms.70075","DOIUrl":"https://doi.org/10.1112/jlms.70075","url":null,"abstract":"<p>By solving the infinitesimal Galilean symmetry for the Korteweg–de Vries (KdV) hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the <i>Galilean symmetry</i> of the KdV hierarchy. As an application, we establish an explicit relationship between the <i>non-abelian Born–Infeld partition function</i> and the <i>generalized Brézin–Gross–Witten partition function</i>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404516","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}

{"title":"Embedding clique subdivisions via crux","authors":"Donglei Yang,&nbsp;Fan Yang","doi":"10.1112/jlms.70073","DOIUrl":"https://doi.org/10.1112/jlms.70073","url":null,"abstract":"&lt;p&gt;For a 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; with average degree &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$d(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and a constant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&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;$alpha &gt;0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we denote by &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;C&lt;/mi&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$C_{alpha }(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; the minimum order of a subgraph &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Hsubseteq G$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&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;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$d(H)geqslant alpha d(G)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Liu and Montgomery conjectured that every 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; contains &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$K_{Omega (t)}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; as a subdivision for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;min&lt;/mi&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msqrt&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380354","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}

{"title":"Discrete quantum subgroups of free unitary quantum groups","authors":"Amaury Freslon,&nbsp;Moritz Weber","doi":"10.1112/jlms.70070","DOIUrl":"https://doi.org/10.1112/jlms.70070","url":null,"abstract":"<p>We classify all compact quantum groups whose C*-algebra sits inside that of the free unitary quantum groups <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>U</mi>\u0000 <mi>N</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <annotation>$U_{N}^{+}$</annotation>\u0000 </semantics></math>. In other words, we classify all discrete quantum subgroups of <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mover>\u0000 <mi>U</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mi>N</mi>\u0000 <mo>+</mo>\u0000 </msubsup>\u0000 <annotation>$widehat{U}_{N}^{+}$</annotation>\u0000 </semantics></math>, thereby proving a quantum variant of Kurosh's theorem to some extent. This yields interesting families which can be described using free wreath products and free complexifications. They can also be seen as quantum automorphism groups of specific quantum graphs which generalize finite rooted regular trees, providing explicit examples of quantum trees.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120186","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}

{"title":"The category of a partitioned fan","authors":"Maximilian Kaipel","doi":"10.1112/jlms.70071","DOIUrl":"https://doi.org/10.1112/jlms.70071","url":null,"abstract":"<p>In this paper the notion of an <i>admissible partition</i> of a simplicial polyhedral fan is introduced and the <i>category of a partitioned fan</i> is defined as a generalisation of the <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-cluster morphism category of a finite-dimensional algebra. This establishes a complete lattice of categories around the <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-cluster morphism category, which is closely tied to the fan structure. We prove that the classifying spaces of these categories are cube complexes, which reduces the process of determining if they are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <mi>π</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$K(pi,1)$</annotation>\u0000 </semantics></math> spaces to three sufficient conditions. We characterise when these conditions are satisfied for fans in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> and prove that the first one, the existence of a certain faithful functor, is satisfied for hyperplane arrangements whose normal vectors lie in the positive orthant. As a consequence, we obtain a new infinite class of algebras for which the <span></span><math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math>-cluster morphism category admits a faithful functor and for which the cube complexes are <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>(</mo>\u0000 <mi>π</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$K(pi,1)$</annotation>\u0000 </semantics></math> spaces. In the final section, we also offer a new algebraic proof of the relationship between an algebra and its <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math>-vector fan.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70071","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119859","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}

{"title":"Mean-field limit of 2D stationary particle systems with signed Coulombian interactions","authors":"Jan Peszek,&nbsp;Rémy Rodiac","doi":"10.1112/jlms.70068","DOIUrl":"https://doi.org/10.1112/jlms.70068","url":null,"abstract":"&lt;p&gt;We study the mean-field limits of critical points of interaction energies with Coulombian singularity. An important feature of our setting is that we allow interaction between particles of opposite signs. Particles of opposite signs attract each other whereas particles of the same signs repel each other. In two dimensional, we prove that the associated empirical measures converge to a limiting measure &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; that satisfies a two-fold criticality condition: in velocity form or in vorticity form. Our setting includes the stationary attraction–repulsion problem with Coulombian singularity and the stationary system of point vortices in fluid mechanics. In this last context, in the case where the limiting measure is in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mtext&gt;loc&lt;/mtext&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$H^{-1}_{text{loc}}(mathbb {R}^2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we recover the classical criticality condition stating that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mo&gt;∇&lt;/mo&gt;\u0000 &lt;mo&gt;⊥&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;*&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$nabla ^perp g ast mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;log&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$g(x)=-log |x|$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, is a stationary solution of the incompressible Euler equation. This result, is, to the best of our knowledge, new in the case of particles with different signs (for particles of the positive sign, it was obtained by Schochet in 1996). In order to derive the limiting criticality condition in the velocity form, we follow an approach devised by Sandier–Serfaty in the context of Ginzburg–Landau vortices. This consists of passing to the limit in the stress-energy tensor associated with the velocity field. On the oth","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114067","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}