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Fundamental Superalgebras with Superinvolution: Exploiting Minimal Varieties 具有超对合的基本超代数：极小变体的开发
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-09-19 DOI: 10.1007/s10468-025-10362-5
Antonio Ioppolo, Elena Pascucci
{"title":"Fundamental Superalgebras with Superinvolution: Exploiting Minimal Varieties","authors":"Antonio Ioppolo,&nbsp;Elena Pascucci","doi":"10.1007/s10468-025-10362-5","DOIUrl":"10.1007/s10468-025-10362-5","url":null,"abstract":"<div><p>This paper extends the concept of <i>fundamental superalgebra</i>, crucial in Kemer’s resolution of the Specht problem, to the framework of superalgebras equipped with a superinvolution. We aim to characterize the class of these special algebras and provide concrete examples. Some of them are developed by exploring connections with varieties of superalgebras with superinvolution which are minimal with respect to their corresponding exponent.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1335 - 1357"},"PeriodicalIF":0.6,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10362-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666043","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
Existence of a New Family of Irreducible Components in the Tensor Product and its Applications 张量积中一类新的不可约分量的存在性及其应用
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-09-17 DOI: 10.1007/s10468-025-10363-4
Rekha Biswal, Stéphane Gaussent
{"title":"Existence of a New Family of Irreducible Components in the Tensor Product and its Applications","authors":"Rekha Biswal,&nbsp;Stéphane Gaussent","doi":"10.1007/s10468-025-10363-4","DOIUrl":"10.1007/s10468-025-10363-4","url":null,"abstract":"<div><p>In this paper, using crystal theory, we establish the existence of a new family of irreducible components arising in the tensor product of two irreducible integrable highest weight modules over symmetrizable Kac–Moody algebras. This work is motivated by the Schur positivity conjecture, Kostant’s conjecture, and Wahl’s conjecture. Furthermore, we prove the Schur positivity conjecture in full generality for finite-dimensional simple Lie algebras under the assumption that <span>(lambda&gt;&gt; mu )</span>; that is, if <span>(lambda )</span> and <span>(mu )</span> are the dominant weights in the tensor product, then <span>(lambda +wmu )</span> remains dominant for all <i>w</i> in the Weyl group.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1315 - 1334"},"PeriodicalIF":0.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10363-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666022","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
Some Properties of the Generalized Foulkes Module 广义Foulkes模的一些性质
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-09-12 DOI: 10.1007/s10468-025-10359-0
Pál Hegedüs, Sai Praveen Madireddi
{"title":"Some Properties of the Generalized Foulkes Module","authors":"Pál Hegedüs,&nbsp;Sai Praveen Madireddi","doi":"10.1007/s10468-025-10359-0","DOIUrl":"10.1007/s10468-025-10359-0","url":null,"abstract":"<div><p>Describing the decomposition of the Foulkes module <span>(F_b^a)</span> into irreducible Specht modules is an open problem when both <span>(a,b &gt; 3)</span>. In this article we provide a new approach for the Generalized Foulkes module <span>(F_{nu }^a)</span> (with arbitrary partition <span>(nu )</span> of <i>b</i>) through its restriction to a maximal Young subgroup <span>({S_b times S_{ab -b}})</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1303 - 1314"},"PeriodicalIF":0.6,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10359-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666039","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
The Fixed Point Locus of the Smooth Jordan Quiver Variety Under the Action of the Finite Subgroups of (textrm{SL}_2(mathbb {C})) 的有限子群作用下光滑约当颤振变化的不动点轨迹 (textrm{SL}_2(mathbb {C}))
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-09-11 DOI: 10.1007/s10468-025-10354-5
Raphaël Paegelow
{"title":"The Fixed Point Locus of the Smooth Jordan Quiver Variety Under the Action of the Finite Subgroups of (textrm{SL}_2(mathbb {C}))","authors":"Raphaël Paegelow","doi":"10.1007/s10468-025-10354-5","DOIUrl":"10.1007/s10468-025-10354-5","url":null,"abstract":"<div><p>In this article, we study the decomposition into irreducible components of the fixed point locus under the action of <span>(Gamma )</span> a finite subgroup of <span>(textrm{SL}_2(mathbb {C}))</span> of the smooth Nakajima quiver variety of the Jordan quiver. The quiver variety associated with the Jordan quiver is either isomorphic to the punctual Hilbert scheme of <span>(mathbb {C}^2)</span> or to the Calogero-Moser space. We describe the irreducible components using quiver varieties over the McKay’s quiver associated with the finite subgroup <span>(Gamma )</span>. We moreover give a general combinatorial model of the indexing set of these irreducible components in terms of certain elements of the root lattice of the affine Lie algebra associated with <span>(Gamma )</span>. Finally, we prove that for every projective, symplectic resolution of a wreath product singularity, there exists an irreducible component of the fixed point locus of the punctual Hilbert scheme of the plane that is isomorphic to the resolution.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1251 - 1286"},"PeriodicalIF":0.6,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666046","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
Counting aCM Toric Bundles of Rank Two on the Veronese Surface 维罗内曲面上2级环面束的计数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-09-11 DOI: 10.1007/s10468-025-10361-6
Yeonjae Hong, Sukmoon Huh
{"title":"Counting aCM Toric Bundles of Rank Two on the Veronese Surface","authors":"Yeonjae Hong,&nbsp;Sukmoon Huh","doi":"10.1007/s10468-025-10361-6","DOIUrl":"10.1007/s10468-025-10361-6","url":null,"abstract":"<div><p>In this paper, we count the number of aCM vector bundles with a toric structure on the Veronese surface, up to a twist by hyperplane divisor class. The main ingredients are the equivalence introduced by A. A. Klyachko between toric vector bundles and certain decreasing filtrations, together with a combinatorial criterion for the vanishing of cohomology derived from this framework.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1287 - 1301"},"PeriodicalIF":0.6,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666038","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
Mirabolically Induced Modules for Loop and Affine ({mathfrak {sl}}_{m}) 环和仿射的代谢诱导模块 ({mathfrak {sl}}_{m})
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-08-21 DOI: 10.1007/s10468-025-10358-1
Fulin Chen, Zhiqiang Li, Shaobin Tan
{"title":"Mirabolically Induced Modules for Loop and Affine ({mathfrak {sl}}_{m})","authors":"Fulin Chen,&nbsp;Zhiqiang Li,&nbsp;Shaobin Tan","doi":"10.1007/s10468-025-10358-1","DOIUrl":"10.1007/s10468-025-10358-1","url":null,"abstract":"<div><p>In this paper, we study the mirabolically induced modules for the loop and affine algebras of <span>(mathfrak {sl}_m)</span>. Among the main results, we give a free field realization of all irreducible mirabolically induced modules, and obtain a character formula for such modules with finite dimensional weight spaces.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1225 - 1250"},"PeriodicalIF":0.6,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666037","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
Twisted Affine Yangian and Rectangular W-algebra of type D D型的扭曲仿射Yangian和矩形w代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-08-20 DOI: 10.1007/s10468-025-10348-3
Mamoru Ueda
{"title":"Twisted Affine Yangian and Rectangular W-algebra of type D","authors":"Mamoru Ueda","doi":"10.1007/s10468-025-10348-3","DOIUrl":"10.1007/s10468-025-10348-3","url":null,"abstract":"<div><p>We define the twisted affine Yangian of type <i>C</i> and construct surjective homomorphisms from twisted affine Yangians of type <i>C</i> to the universal enveloping algebra of the rectangular <i>W</i>-algebra associated with <span>(mathfrak {so}(ln))</span> and a nilpotent element whose Jordan form corresponds to the partition <span>((l^n))</span> in the case when <i>l</i> and <i>n</i> are even.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 5","pages":"1195 - 1224"},"PeriodicalIF":0.6,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145666036","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
The Lie Superalgebra of Transpositions 调换的李超代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-08-13 DOI: 10.1007/s10468-025-10357-2
Christopher M. Drupieski, Jonathan R. Kujawa
{"title":"The Lie Superalgebra of Transpositions","authors":"Christopher M. Drupieski,&nbsp;Jonathan R. Kujawa","doi":"10.1007/s10468-025-10357-2","DOIUrl":"10.1007/s10468-025-10357-2","url":null,"abstract":"<div><p>We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1159 - 1194"},"PeriodicalIF":0.6,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929295","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
Quiver Grassmannians for the Bott-Samelson Resolution of Type A Schubert Varieties 舒伯特A型品种botsamelson分解的Quiver Grassmannians
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-08-11 DOI: 10.1007/s10468-025-10356-3
Giulia Iezzi
{"title":"Quiver Grassmannians for the Bott-Samelson Resolution of Type A Schubert Varieties","authors":"Giulia Iezzi","doi":"10.1007/s10468-025-10356-3","DOIUrl":"10.1007/s10468-025-10356-3","url":null,"abstract":"<div><p>We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a <i>geometrically compatible</i> decomposition for any permutation in the symmetric group <span>(S_n)</span>. For smooth type A Schubert varieties, we identify a suitable dimension vector such that the corresponding quiver Grassmannian is isomorphic to the Schubert variety. To obtain these isomorphisms, we construct a special quiver with relations and investigate two classes of quiver Grassmannians for this quiver.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1139 - 1158"},"PeriodicalIF":0.6,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10356-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929291","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
Dual Coalgebras of Twisted Tensor Products 扭张量积的对偶代数
IF 0.6 4区 数学
Algebras and Representation Theory Pub Date : 2025-08-01 DOI: 10.1007/s10468-025-10353-6
Manuel L. Reyes
{"title":"Dual Coalgebras of Twisted Tensor Products","authors":"Manuel L. Reyes","doi":"10.1007/s10468-025-10353-6","DOIUrl":"10.1007/s10468-025-10353-6","url":null,"abstract":"<div><p>We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we specialize this condition to particular constructions including Ore extensions, smash product algebras, and bitwisted tensor products of bialgebras.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1093 - 1123"},"PeriodicalIF":0.6,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10353-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929287","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
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