Journal of the London Mathematical Society-Second Series最新文献_第7页

Fine multidegrees, universal Gröbner bases, and matrix Schubert varieties 精细多度，通用Gröbner碱基，和矩阵舒伯特品种

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-24 DOI: 10.1112/jlms.70647

Daoji Huang, Matt Larson

{"title":"Fine multidegrees, universal Gröbner bases, and matrix Schubert varieties","authors":"Daoji Huang, Matt Larson","doi":"10.1112/jlms.70647","DOIUrl":"https://doi.org/10.1112/jlms.70647","url":null,"abstract":"We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <annotation>$(mathbb {P}^1)^N$</annotation>\u0000 </semantics></math>. This criterion can be used to give simple proofs of several existing results on universal Gröbner bases. We introduce fine Schubert polynomials, which record the multidegrees of the closures of matrix Schubert varieties in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </msup>\u0000 <annotation>$(mathbb {P}^1)^{n^2}$</annotation>\u0000 </semantics></math>. We compute the fine Schubert polynomials of permutations <math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math> where the coefficients of the Schubert polynomials of <math>\u0000 <semantics>\u0000 <mi>w</mi>\u0000 <annotation>$w$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>w</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$w^{-1}$</annotation>\u0000 </semantics></math> are all either 0 or 1, and we use this to give a universal Gröbner basis for the ideal of the matrix Schubert variety of such a permutation.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70647","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615940","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

Lattice vertex superalgebras and their modules over fields of prime characteristic 素数特征域上的格点超代数及其模

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-24 DOI: 10.1112/jlms.70653

Hongju Zhao, Qiang Mu

{"title":"Lattice vertex superalgebras and their modules over fields of prime characteristic","authors":"Hongju Zhao, Qiang Mu","doi":"10.1112/jlms.70653","DOIUrl":"https://doi.org/10.1112/jlms.70653","url":null,"abstract":"We study lattice vertex superalgebras over an algebraically closed field <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathbb {F}$</annotation>\u0000 </semantics></math> of prime characteristic <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> using the integral form theory. We first use the integral forms of the lattice vertex superalgebra <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mi>L</mi>\u0000 </msub>\u0000 <annotation>$V_L$</annotation>\u0000 </semantics></math>, denoted by <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$V_{L,mathbb {Z}}$</annotation>\u0000 </semantics></math> (due to Dong and Griess), and of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mi>L</mi>\u0000 </msub>\u0000 <annotation>$V_{L}$</annotation>\u0000 </semantics></math>-modules, to characterize the modular lattice vertex superalgebra <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 </msub>\u0000 <msub>\u0000 <mo>⊗</mo>\u0000 <mi>Z</mi>\u0000 </msub>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 <annotation>$V_{L,mathbb {F}} = V_{L,mathbb {Z}} otimes _{mathbb {Z}} mathbb {F}$</annotation>\u0000 </semantics></math> and its modules. More precisely, we provide the generating sets, obtain a bilinear form on <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi>F</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$V_{L,mathbb {F}}$</annotation>\u0000 </semantics></math>, and determine the simplicity of <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>,</mo>\u0000 <mi","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615954","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

The Zarankiewicz problem on tripartite graphs 三部图上的Zarankiewicz问题

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-13 DOI: 10.1112/jlms.70621

Francesco Di Braccio, Freddie Illingworth

{"title":"The Zarankiewicz problem on tripartite graphs","authors":"Francesco Di Braccio, Freddie Illingworth","doi":"10.1112/jlms.70621","DOIUrl":"https://doi.org/10.1112/jlms.70621","url":null,"abstract":"In 1975, Bollobás, Erdős, and Szemerédi asked for the smallest <math>\u0000 <semantics>\u0000 <mi>τ</mi>\u0000 <annotation>$tau$</annotation>\u0000 </semantics></math> such that an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>×</mo>\u0000 <mi>n</mi>\u0000 <mo>×</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$n times n times n$</annotation>\u0000 </semantics></math> tripartite graph with minimum degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <annotation>$n + tau$</annotation>\u0000 </semantics></math> must contain <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$K_{t, t, t}$</annotation>\u0000 </semantics></math>, conjecturing that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 <mo>=</mo>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$tau = mathcal {O}(n^{1/2})$</annotation>\u0000 </semantics></math> for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$t = 2$</annotation>\u0000 </semantics></math>. We prove that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 <mo>=</mo>\u0000 <mi>O</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$tau = mathcal {O}(n^{1 - 1/t})$</","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70621","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615446","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

Representation theory of hereditary artin algebras of finite representation type 有限表示型遗传artin代数的表示理论

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-08 DOI: 10.1112/jlms.70615

Shiping Liu, Gordana Todorov

{"title":"Representation theory of hereditary artin algebras of finite representation type","authors":"Shiping Liu, Gordana Todorov","doi":"10.1112/jlms.70615","DOIUrl":"https://doi.org/10.1112/jlms.70615","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math> be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander–Reiten quiver <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>mod</mi>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$hbox{$mathit {Gamma }_{hspace{0.8pt}{rm mod}H}$}$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>${rm mod}hspace{0.3pt}H$</annotation>\u0000 </semantics></math>, the category of finitely generated left <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math>-modules. This enables us to obtain an effective method to construct <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Γ</mi>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>mod</mi>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$hbox{$mathit {Gamma }_{hspace{0.8pt}{rm mod}H}$}$</annotation>\u0000 </semantics></math> by simply viewing the ext-quiver of <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$H$</annotation>\u0000 </semantics></math>. As easy applications, we compute the numbers of nonisomorphic indecomposable objects in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>${rm mod}hspace{0.3pt}H$</annotation>\u0000 </semantics></math> and the associated cluster category <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>H</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_H$</annotation>\u0000 </semantics></math>, as well as the nilpotency of the radical of each of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>${rm mod}hspace{0.3pt}Hhspace{-0.4pt}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>D</mi>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466807","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

Extremal rate of convergence in continuous dynamics 连续动力学中的极限收敛速度

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-08 DOI: 10.1112/jlms.70627

Francisco J. Cruz-Zamorano, Konstantinos Zarvalis

引用次数: 0

Null projections and noncommutative function theory in operator algebras 算子代数中的零投影与非交换函数理论

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-07 DOI: 10.1112/jlms.70630

David P. Blecher, Raphaël Clouâtre

{"title":"Null projections and noncommutative function theory in operator algebras","authors":"David P. Blecher, Raphaël Clouâtre","doi":"10.1112/jlms.70630","DOIUrl":"https://doi.org/10.1112/jlms.70630","url":null,"abstract":"We study projections in the bidual of a <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^*$</annotation>\u0000 </semantics></math>-algebra <math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> that are null with respect to a subalgebra <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>, that is, projections <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mo>∗</mo>\u0000 <mo>∗</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$pin B^{**}$</annotation>\u0000 </semantics></math> satisfying <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>φ</mi>\u0000 <mo>|</mo>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$|varphi |(p)=0$</annotation>\u0000 </semantics></math> for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>B</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$varphi in B^*$</annotation>\u0000 </semantics></math> annihilating <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>. In the separable case, <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-null projections are precisely the peak projections in the bidual of <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> at which the subalgebra <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> interpolates the entire <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70630","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466658","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

Affine hypersurfaces and superintegrable systems 仿射超曲面与超可积系统

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-07 DOI: 10.1112/jlms.70618

Vicente Cortés, Andreas Vollmer

{"title":"Affine hypersurfaces and superintegrable systems","authors":"Vicente Cortés, Andreas Vollmer","doi":"10.1112/jlms.70618","DOIUrl":"https://doi.org/10.1112/jlms.70618","url":null,"abstract":"It was recently shown that under mild assumptions, second-order conformally superintegrable systems can be encoded in a (0,3)-tensor, called structure tensor. For abundant systems, this approach led to algebraic integrability conditions that essentially allow one to restore a system from the knowledge of its structure tensor in a point on the manifold. Here, we study the geometric structure formalising such systems, which we call an abundant manifold. The underlying Riemannian manifold is necessarily conformally flat. We establish a correspondence between these superintegrable systems and the geometry of affine hypersurfaces. More precisely, we show that abundant manifolds correspond to certain non-degenerate relative affine hypersurface normalisations in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{n+1}$</annotation>\u0000 </semantics></math> (<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 2$</annotation>\u0000 </semantics></math>). We also formulate the necessary and sufficient conditions non-degenerate relative affine hypersurface normalisations in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{n+1}$</annotation>\u0000 </semantics></math> need to satisfy, if they arise from abundant manifolds. These relative affine hypersurface normalisations are called abundant hypersurface normalisations. Both for abundant manifolds and for relative affine hypersurface normalisations a natural concept of conformal equivalence can be defined. We prove that they are compatible, permitting us to identify conformal classes of abundant manifolds with abundant hypersurface immersions (without specified normalisation).","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70618","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148462846","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

On exotic matrix exponential sums and Bessel–Speh functions 奇异矩阵指数和与贝塞尔函数

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-07 DOI: 10.1112/jlms.70619

Elad Zelingher

{"title":"On exotic matrix exponential sums and Bessel–Speh functions","authors":"Elad Zelingher","doi":"10.1112/jlms.70619","DOIUrl":"https://doi.org/10.1112/jlms.70619","url":null,"abstract":"In a previous work with Carmon, we defined Bessel–Speh functions. These are matrix coefficients of irreducible Speh representations of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>GL</mi>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>F</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{GL}_{kc}(mathbb {F})$</annotation>\u0000 </semantics></math>, where <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$mathbb {F}$</annotation>\u0000 </semantics></math> is a finite field. They arise from <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>c</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(k,c)$</annotation>\u0000 </semantics></math> models, which are models that generalize the Whittaker model to Speh representations attached to irreducible generic representations. These constructions are finite field analogs of objects arising naturally in the generalized doubling method over <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic fields, a recently active area of the Langlands program. In this article we study special values of Bessel–Speh functions which were used in our previous work with Carmon to define Ginzburg–Kaplan gamma factors. Our main result computes the special values of interest explicitly in terms of new arithmetic objects we introduce, called exotic matrix Kloosterman sums, which generalize both Katz's exotic Kloosterman sums and twisted matrix Kloosterman sums. We then show that exotic matrix Kloosterman sums can be expressed as products of modified Hall–Littlewood polynomials evaluated at roots of the characteristic polynomial of the Frobenius acting on Katz's exotic Kloosterman sheaf. As an application of our results, we establish new identities for Bessel functions of irreducible generic representations.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70619","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466657","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

Abelian threefolds with imaginary multiplication 带虚乘法的阿贝尔三折

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-06 DOI: 10.1112/jlms.70591

Francesc Fité, Pip Goodman

{"title":"Abelian threefolds with imaginary multiplication","authors":"Francesc Fité, Pip Goodman","doi":"10.1112/jlms.70591","DOIUrl":"https://doi.org/10.1112/jlms.70591","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> be an abelian threefold defined over a number field <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> with potential multiplication by an imaginary quadratic field <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>. Under mild assumptions on <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>, if <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> has signature (2,1) and the multiplication by <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is defined over <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$KM$</annotation>\u0000 </semantics></math>, we attach to <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> an elliptic curve defined over <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> with potential complex multiplication by <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, whose attached Galois representation is determined by the Hecke character associated to the determinant of the compatible system of <math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math>-adic representations of <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>. We deduce that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mo>End</mo>\u0000 <mn>0</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mover>\u0000 <mi>K</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 </msub>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148462961","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

Edge subdivisions and the L 2 $L^2$ -homology of right-angled Coxeter groups 直角Coxeter群的边细分与l2 $L^2$ -同调

IF 1.4 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2026-07-06 DOI: 10.1112/jlms.70626

Grigori Avramidi, Boris Okun, Kevin Schreve

{"title":"Edge subdivisions and the \u0000 \u0000 \u0000 L\u0000 2\u0000 \u0000 $L^2$\u0000 -homology of right-angled Coxeter groups","authors":"Grigori Avramidi, Boris Okun, Kevin Schreve","doi":"10.1112/jlms.70626","DOIUrl":"https://doi.org/10.1112/jlms.70626","url":null,"abstract":"If <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is a flag triangulation of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$S^{n-1}$</annotation>\u0000 </semantics></math>, then the Davis complex <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Σ</mi>\u0000 <mi>L</mi>\u0000 </msub>\u0000 <annotation>$Sigma _L$</annotation>\u0000 </semantics></math> for the associated right-angled Coxeter group (RACG) <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>W</mi>\u0000 <mi>L</mi>\u0000 </msub>\u0000 <annotation>$W_L$</annotation>\u0000 </semantics></math> is a contractible <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-manifold. A special case of a conjecture of Singer predicts that the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-homology of such <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Σ</mi>\u0000 <mi>L</mi>\u0000 </msub>\u0000 <annotation>$Sigma _L$</annotation>\u0000 </semantics></math> vanishes outside the middle dimension. We give conditions which guarantee this vanishing is preserved under edge subdivision of <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>. In particular, we verify Singer's conjecture when <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math> is the barycentric subdivision of the boundary of an <math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-simplex and for general barycentric subdivisions of triangulations of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$S^{2n-1}$</annotation>\u0000 </semantics></math>. Using this, we construct explicit counterexamples to a torsion-growth analogue of Singer's conjecture.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"114 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148462848","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