华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (6): 1-8.doi: 10.3969/j.issn.1000-5641.2014.06.001

• 应用数学与基础数学 •    下一篇

量子Schur超代数与有限一般线性群(英)

陈晓煜,王建磐     

  1. 华东师范大学  数学系, 上海 200241
  • 出版日期:2014-11-25 发布日期:2015-02-07
  • 通讯作者: 王建磐, 男, 教授, 研究方向为代数群与量子群. E-mail:jpwang@ecnu.edu.cn
  • 基金资助:

    国家自然科学基金(11131001)

Quantum Schur superalgebras and finite general linear groups

 CHEN  Xiao-Yu, WANG  Jian-Pan   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Online:2014-11-25 Published:2015-02-07

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摘要： 本文把量子Schur超代数实现为有限域上的一般线性群的某些表示的自同态代数, 推广了Beilinson, Lusztig和MacPherson所建立并在Deng, Du, Parshall和Wang的专著《Finite Dimensional Algebrasand Quantum Groups》中进行细节描述的量子Schur代数与有限一般线性群之间的关系.

关键词: 量子Schur超代数, 有限一般线性群, Steinberg表示

Abstract: This paper realizes quantum Schur superalgebras as the endomorphism algebras of certain representations of general linear groups
over finite fields, generalizing the relationship between quantum Schur algebras and finite general linear groups established by Beilinson, Lusztig, and MacPherson and described in details in the monograph Finite Dimensional Algebras and Quantum Groups by Deng, Du, Parshall, and Wang.

Key words: quantum Schur superalgebra, finite general linear group, Steinberg representation

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