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A periodicity theorem for extensions of Weyl modules 韦尔模块扩展的周期性定理
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-06-16 DOI: 10.1007/s00209-024-03521-9
Mihalis Maliakas, Dimitra-Dionysia Stergiopoulou
{"title":"A periodicity theorem for extensions of Weyl modules","authors":"Mihalis Maliakas, Dimitra-Dionysia Stergiopoulou","doi":"10.1007/s00209-024-03521-9","DOIUrl":"https://doi.org/10.1007/s00209-024-03521-9","url":null,"abstract":"<p>In this paper, we study periodicity phenomena for modular extensions between Weyl modules and between Weyl and simple modules of the general linear group that are associated to adding a power of the characteristic to the first parts of the involved partitions.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141522683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Optimal embeddings for Triebel–Lizorkin and Besov spaces on quasi-metric measure spaces 准度量空间上的 Triebel-Lizorkin 和 Besov 空间的最佳嵌入
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-06-05 DOI: 10.1007/s00209-024-03510-y
Ryan Alvarado, Dachun Yang, Wen Yuan
{"title":"Optimal embeddings for Triebel–Lizorkin and Besov spaces on quasi-metric measure spaces","authors":"Ryan Alvarado, Dachun Yang, Wen Yuan","doi":"10.1007/s00209-024-03510-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03510-y","url":null,"abstract":"<p>In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Hajłasz–Triebel–Lizorkin and Hajłasz–Besov spaces in the general context of quasi-metric measure spaces for an optimal range of the smoothness parameter <i>s</i>. An interesting facet of this work is how the range of <i>s</i> for which the above characterizations of these embeddings hold is intimately linked (in a quantitative manner) to the geometric makeup of the underlying space. Importantly, although the main results in this article are stated in the context of quasi-metric spaces, the authors provide several examples illustrating how this range of <i>s</i> is strictly larger than similar ones currently appearing in the literature, even in the metric setting. Moreover, the authors relate these values of <i>s</i> to the (non)triviality of these function spaces.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On Furusho’s analytic continuation of Drinfeld logarithms 关于古庄的德林费尔德对数解析延续
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-06-03 DOI: 10.1007/s00209-024-03522-8
Yen-Tsung Chen
{"title":"On Furusho’s analytic continuation of Drinfeld logarithms","authors":"Yen-Tsung Chen","doi":"10.1007/s00209-024-03522-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03522-8","url":null,"abstract":"<p>In the present paper, we establish an analytic continuation of Drinfeld logarithms by using the techniques introduced in Furusho (Tunis J Math 4(3):559–586, 2022) . This result can be seen as an analogue of the analytic continuation of the elliptic integrals of the first kind for Drinfeld modules.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"32 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Statistics for anticyclotomic Iwasawa invariants of elliptic curves 椭圆曲线反周岩泽不变式统计
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-06-03 DOI: 10.1007/s00209-024-03517-5
Jeffrey Hatley, Debanjana Kundu, Anwesh Ray
{"title":"Statistics for anticyclotomic Iwasawa invariants of elliptic curves","authors":"Jeffrey Hatley, Debanjana Kundu, Anwesh Ray","doi":"10.1007/s00209-024-03517-5","DOIUrl":"https://doi.org/10.1007/s00209-024-03517-5","url":null,"abstract":"<p>We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves, considered over anticyclotomic <span>(mathbb {Z}_p)</span>-extensions in both the definite and indefinite settings. The results in this paper lie at the intersection of arithmetic statistics and Iwasawa theory.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"16 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The conjugate uniformization via 1-motives 通过单动量的共轭均匀化
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-06-02 DOI: 10.1007/s00209-024-03523-7
Sean Howe, Jackson S. Morrow, Peter Wear
{"title":"The conjugate uniformization via 1-motives","authors":"Sean Howe, Jackson S. Morrow, Peter Wear","doi":"10.1007/s00209-024-03523-7","DOIUrl":"https://doi.org/10.1007/s00209-024-03523-7","url":null,"abstract":"<p>We use the <i>p</i>-divisible group attached to a 1-motive to generalize the conjugate <i>p</i>-adic uniformization of Iovita–Morrow–Zaharescu to arbitrary <i>p</i>-adic formal semi-abelian schemes or <i>p</i>-divisible groups over the ring of integers in a <i>p</i>-adic field. This mirrors a mixed Hodge theory construction of the inverse uniformization map for complex semi-abelian varieties.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"63 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Morse theory on Lie groupoids 李群上的莫尔斯理论
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-31 DOI: 10.1007/s00209-024-03525-5
Cristian Ortiz, Fabricio Valencia
{"title":"Morse theory on Lie groupoids","authors":"Cristian Ortiz, Fabricio Valencia","doi":"10.1007/s00209-024-03525-5","DOIUrl":"https://doi.org/10.1007/s00209-024-03525-5","url":null,"abstract":"<p>In this paper we introduce Morse Lie groupoid morphisms and study their main properties. We show that this notion is Morita invariant which gives rise to a well defined notion of Morse function on differentiable stacks. We show a groupoid version of the Morse lemma which is used to describe the topological behavior of the critical subgroupoid levels of a Morse Lie groupoid morphism around its nondegenerate critical orbits. We also prove Morse type inequalities for certain separated differentiable stacks and construct a Morse double complex whose total cohomology is isomorphic to the Bott–Shulman–Stasheff cohomology of the underlying Lie groupoid. We provide several examples and applications.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"36 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Structure constants in equivariant oriented cohomology of flag varieties 旗变体等变定向同调中的结构常数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-30 DOI: 10.1007/s00209-024-03485-w
Rebecca Goldin, Changlong Zhong
{"title":"Structure constants in equivariant oriented cohomology of flag varieties","authors":"Rebecca Goldin, Changlong Zhong","doi":"10.1007/s00209-024-03485-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03485-w","url":null,"abstract":"<p>We introduce generalized Demazure operators for the equivariant oriented cohomology of the flag variety, which have specializations to various Demazure operators and Demazure–Lusztig operators in both equivariant cohomology and equivariant K-theory. In the context of the geometric basis of the equivariant oriented cohomology given by certain Bott–Samelson classes, we use these operators to obtain formulas for the structure constants arising in different bases. Specializing to divided difference operators and Demazure operators in singular cohomology and K-theory, we recover the formulas for structure constants of Schubert classes obtained in Goldin and Knutson (Pure Appl Math Q 17(4):1345–1385, 2021). Two specific specializations result in formulas for the the structure constants for cohomological and K-theoretic stable bases as well; as a corollary we reproduce a formula for the structure constants of the Segre–Schwartz–MacPherson basis previously obtained by Su (Math Zeitschrift 298:193–213, 2021). Our methods involve the study of the formal affine Demazure algebra, providing a purely algebraic proof of these results.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"35 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Transitivity in finite general linear groups 有限一般线性群中的传递性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-30 DOI: 10.1007/s00209-024-03511-x
Alena Ernst, Kai-Uwe Schmidt
{"title":"Transitivity in finite general linear groups","authors":"Alena Ernst, Kai-Uwe Schmidt","doi":"10.1007/s00209-024-03511-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03511-x","url":null,"abstract":"<p>It is known that the notion of a transitive subgroup of a permutation group <i>G</i> extends naturally to subsets of <i>G</i>. We consider subsets of the general linear group <span>({{,textrm{GL},}}(n,q))</span> acting transitively on flag-like structures, which are common generalisations of <i>t</i>-dimensional subspaces of <span>(mathbb {F}_q^n)</span> and bases of <i>t</i>-dimensional subspaces of <span>(mathbb {F}_q^n)</span>. We give structural characterisations of transitive subsets of <span>({{,textrm{GL},}}(n,q))</span> using the character theory of <span>({{,textrm{GL},}}(n,q))</span> and interpret such subsets as designs in the conjugacy class association scheme of <span>({{,textrm{GL},}}(n,q))</span>. In particular we generalise a theorem of Perin on subgroups of <span>({{,textrm{GL},}}(n,q))</span> acting transitively on <i>t</i>-dimensional subspaces. We survey transitive subgroups of <span>({{,textrm{GL},}}(n,q))</span>, showing that there is no subgroup of <span>({{,textrm{GL},}}(n,q))</span> with <span>(1&lt;t&lt;n)</span> acting transitively on <i>t</i>-dimensional subspaces unless it contains <span>({{,textrm{SL},}}(n,q))</span> or is one of two exceptional groups. On the other hand, for all fixed <i>t</i>, we show that there exist nontrivial subsets of <span>({{,textrm{GL},}}(n,q))</span> that are transitive on linearly independent <i>t</i>-tuples of <span>(mathbb {F}_q^n)</span>, which also shows the existence of nontrivial subsets of <span>({{,textrm{GL},}}(n,q))</span> that are transitive on more general flag-like structures. We establish connections with orthogonal polynomials, namely the Al-Salam–Carlitz polynomials, and generalise a result by Rudvalis and Shinoda on the distribution of the number of fixed points of the elements in <span>({{,textrm{GL},}}(n,q))</span>. Many of our results can be interpreted as <i>q</i>-analogs of corresponding results for the symmetric group.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration 临界平面薛定谔-泊松方程：存在性、多重性和集中性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-30 DOI: 10.1007/s00209-024-03520-w
Yiqing Li, Vicenţiu D. Rădulescu, Binlin Zhang
{"title":"Critical planar Schrödinger–Poisson equations: existence, multiplicity and concentration","authors":"Yiqing Li, Vicenţiu D. Rădulescu, Binlin Zhang","doi":"10.1007/s00209-024-03520-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03520-w","url":null,"abstract":"<p>In this paper, we are concerned with the study of the following 2-D Schrödinger–Poisson equation with critical exponential growth </p><span>$$begin{aligned} -varepsilon ^2Delta u+V(x)u+varepsilon ^{-alpha }(I_alpha *|u|^q)|u|^{q-2}u=f(u), end{aligned}$$</span><p>where <span>(varepsilon &gt;0)</span> is a parameter, <span>(I_alpha )</span> is the Riesz potential, <span>(0&lt;alpha &lt;2)</span>, <span>(Vin {mathcal {C}}({{mathbb {R}}}^2,{{mathbb {R}}}))</span>, and <span>(fin {mathcal {C}}({{mathbb {R}}},{{mathbb {R}}}))</span> satisfies the critical exponential growth. By variational methods, we first prove the existence of ground state solutions for the above system with the periodic potential. Then we obtain that there exists a positive ground state solution of the above system concentrating at a global minimum of <i>V</i> in the semi-classical limit under some suitable conditions. Meanwhile, the exponential decay of this ground state solution is detected. Finally, we establish the multiplicity of positive solutions by using the Ljusternik–Schnirelmann theory.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Coarse equivalence versus bijective coarse equivalence of expander graphs 扩展图的粗等价性与双射粗等价性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-05-30 DOI: 10.1007/s00209-024-03512-w
Florent P. Baudier, Bruno M. Braga, Ilijas Farah, Alessandro Vignati, Rufus Willett
{"title":"Coarse equivalence versus bijective coarse equivalence of expander graphs","authors":"Florent P. Baudier, Bruno M. Braga, Ilijas Farah, Alessandro Vignati, Rufus Willett","doi":"10.1007/s00209-024-03512-w","DOIUrl":"https://doi.org/10.1007/s00209-024-03512-w","url":null,"abstract":"<p>We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras of coarse disjoint unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"61 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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