Deligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups

Author:

Comes Jonathan,Wilson Benjamin

Abstract

We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric Schur polynomials, and give a method for decomposing their tensor products. Along the way, we describe indecomposable objects in Re _ p ( G L δ ) \underline {\operatorname {Re}}\!\operatorname {p}(GL_\delta ) and explain how to decompose their tensor products.

Publisher

American Mathematical Society (AMS)

Subject

Mathematics (miscellaneous)

Reference28 articles.

1. Graduate Texts in Mathematics;Anderson, Frank W.,1992

2. Tensor product representations of general linear groups and their connections with Brauer algebras;Benkart, Georgia;J. Algebra,1994

3. Cambridge Studies in Advanced Mathematics;Benson, D. J.,1991

4. Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras;Berele, A.;Adv. in Math.,1987

5. Gradings on walled Brauer algebras and Khovanov’s arc algebra;Brundan, Jonathan;Adv. Math.,2012

Cited by 36 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Diagrammatics for real supergroups;Annals of Representation Theory;2024-05-31

2. Gaudin model and Deligne’s category;Letters in Mathematical Physics;2023-12-19

3. Weighted Colimits of 2-Representations and Star Algebras;Applied Categorical Structures;2023-07-22

4. THE QUANTUM ISOMERIC SUPERCATEGORY;Journal of the Institute of Mathematics of Jussieu;2023-04-25

5. On classical tensor categories attached to the irreducible representations of the general linear supergroups $$GL(n\vert n)$$;Selecta Mathematica;2023-04-20

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3