发布求助
文献互助 智能选刊 最新文献

Algebras and Representation Theory最新文献

筛选
英文 中文
Highest Weight Modules for Affine and Loop Superalgebras of (mathfrak {osp}_{1|2}(mathbb C)) 的仿射超代数和环超代数的最大权模 (mathfrak {osp}_{1|2}(mathbb C))
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-28 DOI: 10.1007/s10468-024-10292-8
Fulin Chen, Xin Huang, Shaobin Tan
{"title":"Highest Weight Modules for Affine and Loop Superalgebras of (mathfrak {osp}_{1|2}(mathbb C))","authors":"Fulin Chen,&nbsp;Xin Huang,&nbsp;Shaobin Tan","doi":"10.1007/s10468-024-10292-8","DOIUrl":"10.1007/s10468-024-10292-8","url":null,"abstract":"<div><p>This paper is about the highest weight module theory for affine superalgebra <span>(widetilde{mathfrak g})</span> of <span>({mathfrak g}={mathfrak {osp}_{1|2}(mathbb C)})</span> and loop superalgebra <span>({mathfrak g}{otimes }{mathbb {C}}[t,t^{-1}])</span>. Among the main results, we obtain (i) a necessary and sufficient condition for Verma type <span>(ell )</span>-highest weight <span>(widetilde{mathfrak g})</span>-modules to be irreducible; (ii) a free field(-like) realization of all irreducible <span>(ell )</span>-highest weight <span>(widetilde{mathfrak g})</span>-modules; (iii) a character formula for all irreducible <span>(ell )</span>-highest weight <span>(widetilde{mathfrak g})</span>-modules with finite dimensional weight spaces. We also obtain three similar results for highest weight <span>({mathfrak g}{otimes }{mathbb {C}}[t,t^{-1}])</span>-modules.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 6","pages":"2099 - 2130"},"PeriodicalIF":0.5,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995695","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
Automorphisms of Quantum Toroidal Algebras from an Action of the Extended Double Affine Braid Group 扩展双仿射编织群作用下量子环面代数的自同构
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-24 DOI: 10.1007/s10468-024-10291-9
Duncan Laurie
{"title":"Automorphisms of Quantum Toroidal Algebras from an Action of the Extended Double Affine Braid Group","authors":"Duncan Laurie","doi":"10.1007/s10468-024-10291-9","DOIUrl":"10.1007/s10468-024-10291-9","url":null,"abstract":"<div><p>We first construct an action of the extended double affine braid group <span>(mathcal {ddot{B}})</span> on the quantum toroidal algebra <span>(U_{q}(mathfrak {g}_{textrm{tor}}))</span> in untwisted and twisted types. As a crucial step in the proof, we obtain a finite Drinfeld new style presentation for a broad class of quantum affinizations. In the simply laced cases, using our action and certain involutions of <span>(mathcal {ddot{B}})</span> we produce automorphisms and anti-involutions of <span>(U_{q}(mathfrak {g}_{textrm{tor}}))</span> which exchange the horizontal and vertical subalgebras. Moreover, they switch the central elements <i>C</i> and <span>(k_{0}^{a_{0}}dots k_{n}^{a_{n}})</span> up to inverse. This can be viewed as the analogue, for these quantum toroidal algebras, of the duality for double affine braid groups used by Cherednik to realise the difference Fourier transform in his celebrated proof of the Macdonald evaluation conjectures. Our work generalises existing results in type <i>A</i> due to Miki which have been instrumental in the study of the structure and representation theory of <span>(U_{q}(mathfrak {sl}_{n+1,textrm{tor}}))</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 6","pages":"2067 - 2097"},"PeriodicalIF":0.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10291-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995845","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 Deformed Tanisaki-Garsia-Procesi Modules 变形Tanisaki-Garsia-Procesi模块
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-20 DOI: 10.1007/s10468-024-10288-4
Maico Freitas, Evgeny Mukhin
{"title":"The Deformed Tanisaki-Garsia-Procesi Modules","authors":"Maico Freitas,&nbsp;Evgeny Mukhin","doi":"10.1007/s10468-024-10288-4","DOIUrl":"10.1007/s10468-024-10288-4","url":null,"abstract":"<div><p>The polynomial ideals studied by A. Garsia and C. Procesi play an important role in the theory of Kostka polynomials. We give multiparameter flat deformations of these ideals and define an action of the extended affine symmetric group on the corresponding quotient algebras multiplied by the sign representation. We show that the images of these modules under the affine Schur-Weyl duality are dual to the local Weyl modules for the loop algebra <span>(mathfrak {sl}_{n+1}[t^{pm 1}])</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 6","pages":"2019 - 2044"},"PeriodicalIF":0.5,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994937","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 Note on Schur-Weyl Dualities for GL(m) and GL(m|n) 关于 GL(m) 和 GL(m|n) 的舒尔-韦尔对偶性的说明
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-17 DOI: 10.1007/s10468-024-10290-w
František Marko
{"title":"A Note on Schur-Weyl Dualities for GL(m) and GL(m|n)","authors":"František Marko","doi":"10.1007/s10468-024-10290-w","DOIUrl":"10.1007/s10468-024-10290-w","url":null,"abstract":"<div><p>We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space and mixed tensor space, respectively, over the group algebra of the symmetric group and the Brauer wall algebra, respectively. Our main new results are the second part of the mixed Schur-Weyl dualities and mixed super Schur-Weyl dualities over an infinite ground field of positive characteristic.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1957 - 1979"},"PeriodicalIF":0.5,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264524","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
Homologically Smooth Connected Cochain DGAs 同源光滑连接共链 DGA
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-09 DOI: 10.1007/s10468-024-10287-5
X.-F. Mao
{"title":"Homologically Smooth Connected Cochain DGAs","authors":"X.-F. Mao","doi":"10.1007/s10468-024-10287-5","DOIUrl":"10.1007/s10468-024-10287-5","url":null,"abstract":"<div><p>Let <span>(mathscr {A})</span> be a connected cochain DG algebra such that <span>(H(mathscr {A}))</span> is a Noetherian graded algebra. We give some criteria for <span>(mathscr {A})</span> to be homologically smooth in terms of the singularity category, the cone length of the canonical module <i>k</i> and the global dimension of <span>(mathscr {A})</span>. For any cohomologically finite DG <span>(mathscr {A})</span>-module <i>M</i>, we show that it is compact when <span>(mathscr {A})</span> is homologically smooth. If <span>(mathscr {A})</span> is in addition Gorenstein, we get </p><div><div><span>$$begin{aligned} textrm{CMreg}M = textrm{depth}_{mathscr {A}}mathscr {A} + mathrm {Ext.reg}, M&lt;infty , end{aligned}$$</span></div></div><p>where <span>(textrm{CMreg}M)</span> is the Castelnuovo-Mumford regularity of <i>M</i>, <span>(textrm{depth}_{mathscr {A}}mathscr {A})</span> is the depth of <span>(mathscr {A})</span> and <span>( mathrm {Ext.reg}, M)</span> is the Ext-regularity of <i>M</i>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1931 - 1955"},"PeriodicalIF":0.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226102","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
Modified Ariki-Koike Algebra and Yokonuma-Hecke like Relations 修正的有熊小池代数和横沼-赫克相似关系
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-09-04 DOI: 10.1007/s10468-024-10286-6
Myungho Kim, Sungsoon Kim
{"title":"Modified Ariki-Koike Algebra and Yokonuma-Hecke like Relations","authors":"Myungho Kim,&nbsp;Sungsoon Kim","doi":"10.1007/s10468-024-10286-6","DOIUrl":"10.1007/s10468-024-10286-6","url":null,"abstract":"<div><p>We find new presentations of the modified Ariki-Koike algebra (known also as Shoji’s algebra) <span>(mathcal {H}_{n,r})</span> over an integral domain <i>R</i> associated with a set of parameters <span>(q,u_1,ldots ,u_r)</span> in <i>R</i>. It turns out that the algebra <span>(mathcal {H}_{n,r})</span> has a set of generators <span>(t_1,ldots ,t_n)</span> and <span>(g_1,ldots g_{n-1})</span> subject to some defining relations similar to the relations of Yokonuma-Hecke algebra. We also obtain a presentation of <span>(mathcal {H}_{n,r})</span> which is independent of the choice of <span>(u_1,ldots u_r)</span>. As applications of the presentations, we find an explicit and direct isomorphism between the modified Ariki-Koike algebras with different choices of parameters <span>((u_1,ldots ,u_r))</span>. We also find an explicit trace form on the algebra <span>(mathcal {H}_{n,r})</span> which is symmetrizing provided the parameters <span>(u_1,ldots , u_r)</span> are invertible in <i>R</i>. We show that the symmetric group <span>(mathfrak {S}(r))</span> acts on the algebra <span>(mathcal H_{n,r})</span>, and find a basis and a set of generators of the fixed subalgebra <span>(mathcal H_{n,r}^{mathfrak {S}(r)})</span>.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1909 - 1930"},"PeriodicalIF":0.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204750","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
Hammocks for Non-Domestic String Algebras 非国内弦理论的吊床
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-08-24 DOI: 10.1007/s10468-024-10285-7
Vinit Sinha, Amit Kuber, Annoy Sengupta, Bhargav Kale
{"title":"Hammocks for Non-Domestic String Algebras","authors":"Vinit Sinha,&nbsp;Amit Kuber,&nbsp;Annoy Sengupta,&nbsp;Bhargav Kale","doi":"10.1007/s10468-024-10285-7","DOIUrl":"10.1007/s10468-024-10285-7","url":null,"abstract":"<div><p>We show that the order type of the simplest version of a hammock for string algebras lies in the class of <i>finite description</i> linear orders–the smallest class of linear orders containing <span>(textbf{0})</span>, <span>(textbf{1})</span>, and that is closed under isomorphisms, finite order sum, anti-lexicographic product with <span>(omega )</span> and <span>(omega ^*)</span>, and shuffle of finite subsets–using condensation (localization) of linear orders as a tool. We also introduce two finite subsets of the set of bands and use them to describe the location of left <span>(mathbb {N})</span>-strings in the completion of hammocks.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1869 - 1908"},"PeriodicalIF":0.5,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204751","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
Translation Hopf Algebras and Hopf Heaps 翻译霍普夫代数和霍普夫堆
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-08-21 DOI: 10.1007/s10468-024-10283-9
Tomasz Brzeziński, Małgorzata Hryniewicka
{"title":"Translation Hopf Algebras and Hopf Heaps","authors":"Tomasz Brzeziński,&nbsp;Małgorzata Hryniewicka","doi":"10.1007/s10468-024-10283-9","DOIUrl":"10.1007/s10468-024-10283-9","url":null,"abstract":"<div><p>To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of a Hopf heap with the translation Hopf algebra isomorphic to the acting Hopf algebra. It is then shown that this assignment establishes an equivalence between categories of Hopf heaps and Hopf-Galois co-objects.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1805 - 1819"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10283-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204752","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
Hopf Algebras with the Dual Chevalley Property of Finite Corepresentation Type 具有有限核心呈现类型双重切瓦利性质的霍普夫代数方程
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-08-21 DOI: 10.1007/s10468-024-10284-8
Jing Yu, Kangqiao Li, Gongxiang Liu
{"title":"Hopf Algebras with the Dual Chevalley Property of Finite Corepresentation Type","authors":"Jing Yu,&nbsp;Kangqiao Li,&nbsp;Gongxiang Liu","doi":"10.1007/s10468-024-10284-8","DOIUrl":"10.1007/s10468-024-10284-8","url":null,"abstract":"<div><p>Let <i>H</i> be a finite-dimensional Hopf algebra over an algebraically closed field <span>(Bbbk )</span> with the dual Chevalley property. We prove that <i>H</i> is of finite corepresentation type if and only if it is coNakayama, if and only if the link quiver <span>(textrm{Q}(H))</span> of <i>H</i> is a disjoint union of basic cycles, if and only if the link-indecomposable component <span>(H_{(1)})</span> containing <span>(Bbbk 1)</span> is a pointed Hopf algebra and the link quiver of <span>(H_{(1)})</span> is a basic cycle.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1821 - 1867"},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226101","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
Quantum Frobenius Splittings and Cluster Structures 量子弗罗贝尼斯分裂和簇结构
IF 0.5 4区 数学
Algebras and Representation Theory Pub Date : 2024-08-05 DOI: 10.1007/s10468-024-10281-x
Jinfeng Song
{"title":"Quantum Frobenius Splittings and Cluster Structures","authors":"Jinfeng Song","doi":"10.1007/s10468-024-10281-x","DOIUrl":"10.1007/s10468-024-10281-x","url":null,"abstract":"<div><p>We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialization, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 5","pages":"1773 - 1797"},"PeriodicalIF":0.5,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141948726","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信