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Plethysm Stability of Schur’s Q-functions 舒尔q函数的体积稳定性
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-02-06 DOI: 10.1007/s10468-026-10375-8
John Graf, Naihuan Jing
{"title":"Plethysm Stability of Schur’s Q-functions","authors":"John Graf,&nbsp;Naihuan Jing","doi":"10.1007/s10468-026-10375-8","DOIUrl":"10.1007/s10468-026-10375-8","url":null,"abstract":"<div><p>Schur functions has been shown to satisfy certain plethysm stability properties and recurrence relations. In this paper, use vertex operator methods to study analogous stability properties of Schur’s <i>Q</i>-functions. Although the two functions have similar stability properties, we find a special case where the plethysm of Schur’s <i>Q</i>-functions exhibits linear increase.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"127 - 151"},"PeriodicalIF":0.6,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-026-10375-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Auslander Algebras of Finite Representation Type 有限表示型的高等Auslander代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-01-24 DOI: 10.1007/s10468-025-10373-2
Shen Li
{"title":"Higher Auslander Algebras of Finite Representation Type","authors":"Shen Li","doi":"10.1007/s10468-025-10373-2","DOIUrl":"10.1007/s10468-025-10373-2","url":null,"abstract":"<div><p>Let <span>(Lambda )</span> be a higher Auslander algebra with global dimension <span>(n+1)</span>. In this paper, we prove that <span>(Lambda )</span> is representation-finite if and only if the number of non-isomorphic indecomposable <span>(Lambda )</span>-modules with projective dimension <span>(n+1)</span> is finite. As an application, we classify the representation-finite higher Auslander algebras of linearly oriented type <span>(mathbb {A})</span> in the sense of Iyama and calculate the number of non-isomorphic indecomposable modules over these algebras.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"111 - 126"},"PeriodicalIF":0.6,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic p-groups 有理群代数的Wedderburn分解的一个组合公式和普通亚环p群的有理表示
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-01-24 DOI: 10.1007/s10468-025-10371-4
Ram Karan Choudhary, Sunil Kumar Prajapati
{"title":"A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras and the Rational Representations of Ordinary Metacyclic p-groups","authors":"Ram Karan Choudhary,&nbsp;Sunil Kumar Prajapati","doi":"10.1007/s10468-025-10371-4","DOIUrl":"10.1007/s10468-025-10371-4","url":null,"abstract":"<div><p>In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic <i>p</i>-group <i>G</i>, where <i>p</i> is any prime. We also provide a formula for counting irreducible rational representations of <i>G</i> with distinct degrees and derive a method to explicitly construct all inequivalent irreducible rational matrix representations of <i>G</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"85 - 109"},"PeriodicalIF":0.6,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Realizing Modular Data from Centers of Near-group Categories 近群类中心数据模块化的实现
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2026-01-13 DOI: 10.1007/s10468-025-10370-5
Zhiqiang Yu, Qing Zhang
{"title":"Realizing Modular Data from Centers of Near-group Categories","authors":"Zhiqiang Yu,&nbsp;Qing Zhang","doi":"10.1007/s10468-025-10370-5","DOIUrl":"10.1007/s10468-025-10370-5","url":null,"abstract":"<div><p>In this paper, we show the existence of a near-group category of type <span>(mathbb {Z} / 4mathbb {Z} times mathbb {Z} / 4mathbb {Z}+16)</span> and compute the modular data of its Drinfeld center. We prove that a modular data of rank 10 can be obtained through a condensation of the Drinfeld center of the near-group category <span>(mathbb {Z} / 4mathbb {Z} times mathbb {Z} / 4mathbb {Z}+16)</span>, and that it can also be realized as the Drinfeld center of a fusion category of rank 4. Moreover, we compute the modular data for the Drinfeld center of a near-group category <span>(mathbb {Z} / 8mathbb {Z}+8)</span> and show that, up to Galois conjugation, the non-pointed factor of its condensation has the same modular data as the quantum group category <span>(mathcal {C}(mathfrak {g}_2, 4))</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"67 - 84"},"PeriodicalIF":0.6,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Preface to the special issue in honor of Peter Littelmann: Representations, Combinatorics and Geometry 纪念彼得·利特曼的特刊前言：表示，组合和几何
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-12-19 DOI: 10.1007/s10468-025-10365-2
Michel Brion, Vyjayanthi Chari, Stéphanie Cupit-Foutou, Stéphane Gaussent
{"title":"Preface to the special issue in honor of Peter Littelmann: Representations, Combinatorics and Geometry","authors":"Michel Brion,&nbsp;Vyjayanthi Chari,&nbsp;Stéphanie Cupit-Foutou,&nbsp;Stéphane Gaussent","doi":"10.1007/s10468-025-10365-2","DOIUrl":"10.1007/s10468-025-10365-2","url":null,"abstract":"","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 6","pages":"1387 - 1389"},"PeriodicalIF":0.6,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10365-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146027155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Recollement Approach to Cauchy Sequences and Cocompact Objects 柯西序列与紧致对象的回溯方法
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-12-11 DOI: 10.1007/s10468-025-10367-0
Nan Gao, Jing Ma, Yuxiao Yang
{"title":"A Recollement Approach to Cauchy Sequences and Cocompact Objects","authors":"Nan Gao,&nbsp;Jing Ma,&nbsp;Yuxiao Yang","doi":"10.1007/s10468-025-10367-0","DOIUrl":"10.1007/s10468-025-10367-0","url":null,"abstract":"<div><p>In the paper, we identify Cauchy sequences and 0-cocompact objects along functors in the recollements of related categories, respectively. As applications in Gorenstein homological algebra, on one hand, the bounded Gorenstein derived categories of algebras of finite Cohen-Macaulay type are characterized as a sequential completion based on Cauchy sequences. On the other hand, the set of 0-cocompact cogenerators for the Gorenstein derived categories of algebras of finite Cohen-Macaulay type are obtained.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"49 - 65"},"PeriodicalIF":0.6,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Maximal Root Subsystems of Affine Reflection Systems and Duality 仿射反射系统的极大根子系统及其对偶性
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-12-09 DOI: 10.1007/s10468-025-10368-z
Irfan Habib
{"title":"Maximal Root Subsystems of Affine Reflection Systems and Duality","authors":"Irfan Habib","doi":"10.1007/s10468-025-10368-z","DOIUrl":"10.1007/s10468-025-10368-z","url":null,"abstract":"<div><p>Any maximal root subsystem of a finite crystallographic reduced root system is either a closed root subsystem or its dual is a closed root subsystem in the dual root system. In this article, we classify the maximal root subsystems of an affine reflection system (reduced and non-reduced) and prove that this closed or dual-closed property holds in much more generality for reduced affine reflection systems. Moreover, we explicitly determine when a maximal root subsystem is a maximal closed root subsystem. Using our classification, at the end, we characterize the maximal root systems of affine reflection systems with nullity less than or equal to 2 using Hermite normal forms; especially for Saito’s EARS of nullity 2. This in turn, in the reduced case, classifies the maximal subgroups of the Weyl group of an affine reflection system that are generated by reflections.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"21 - 47"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10368-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147337868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Automating the Stable Rank Computation for Special Biserial Algebras 特殊双列代数稳定秩计算的自动化
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-11-28 DOI: 10.1007/s10468-025-10366-1
Suyash Srivastava, Amit Kuber
{"title":"Automating the Stable Rank Computation for Special Biserial Algebras","authors":"Suyash Srivastava,&nbsp;Amit Kuber","doi":"10.1007/s10468-025-10366-1","DOIUrl":"10.1007/s10468-025-10366-1","url":null,"abstract":"<div><p>Given a special biserial algebra <span>(Lambda )</span> over an algebraically closed field, let <span>(text {rad}_Lambda )</span> denote the radical of its module category. The authors showed with Sinha that the stable rank of a special biserial algebra <span>(Lambda )</span>, i.e., the least ordinal <span>(gamma )</span> satisfying <span>(text {rad}_Lambda ^gamma =text {rad}_Lambda ^{gamma +1})</span>, is strictly bounded above by <span>(omega ^2)</span>. We use finite automata to give simple algorithmic proofs, complete with their time complexity analyses, of two key ingredients in the proof of this result–the first one states that certain linear orders called hammocks associated with such algebras are <i>finite description linear orders</i>, i.e., they lie in the smallest class of linear orders that contains finite linear orders and <span>(omega )</span>, and that is closed under isomorphisms, order-reversals, binary sums, co-lexicographic products and finitary shuffles. We also document a complete proof of the result that the class of order types(=order-isomorphism classes) of finite description linear orders coincides with that of languages of finite automata under inorder.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"29 1","pages":"1 - 20"},"PeriodicalIF":0.6,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147342700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Tensor Hierarchy Algebras and Restricted Associativity 张量层次代数与限制结合律
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-10-09 DOI: 10.1007/s10468-025-10360-7
Martin Cederwall, Jakob Palmkvist
{"title":"Tensor Hierarchy Algebras and Restricted Associativity","authors":"Martin Cederwall,&nbsp;Jakob Palmkvist","doi":"10.1007/s10468-025-10360-7","DOIUrl":"10.1007/s10468-025-10360-7","url":null,"abstract":"<div><p>We study local algebras, which are structures similar to <span>(mathbb {Z})</span>-graded algebras concentrated in degrees <span>(-1,0,1)</span>, but without a product defined for pairs of elements at the same degree <span>(pm 1)</span>. To any triple consisting of a Kac–Moody algebra <span>({mathfrak g})</span> with an invertible and symmetrisable Cartan matrix, a dominant integral weight of <span>({mathfrak g})</span> and an invariant symmetric bilinear form on <span>({mathfrak g})</span>, we associate a local algebra satisfying a restricted version of associativity. From it, we derive a local Lie superalgebra by a commutator construction. Under certain conditions, we identify generators which we show satisfy the relations of the tensor hierarchy algebra <i>W</i> previously defined from the same data. The result suggests that an underlying structure satisfying such a restricted associativity may be useful in applications of tensor hierarchy algebras to extended geometry.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1369 - 1385"},"PeriodicalIF":0.6,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10360-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Blow-up of a Generalized Flag Variety 广义标志品种的放大
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-10-04 DOI: 10.1007/s10468-025-10364-3
Indranil Biswas, Pinakinath Saha
{"title":"Blow-up of a Generalized Flag Variety","authors":"Indranil Biswas,&nbsp;Pinakinath Saha","doi":"10.1007/s10468-025-10364-3","DOIUrl":"10.1007/s10468-025-10364-3","url":null,"abstract":"<div><p>Let <i>G</i> be a connected simply connected semisimple complex algebraic group and <span>(P, subset , G)</span> a parabolic subgroup. We give a necessary and sufficient condition for a line bundle — on the blow-up of the generalized flag variety <i>G</i>/<i>P</i> along a smooth Schubert variety — to be ample (respectively, nef). Furthermore, it is shown that every such nef line bundle is actually globally generated. As a consequence, we are able to describe when such a blow-up is (weak) Fano.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1359 - 1368"},"PeriodicalIF":0.6,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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