华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 3: 18 - 24,45

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.03.002

数学

sl(n+1)的次正则幂零表示的同态空间

  • 李宜阳 ,
  • 舒斌 ,
  • 叶刚
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  • 1. 上海工程技术大学 数理与统计学院, 上海 201620;
    2. 华东师范大学 数学科学学院, 上海 200241
李宜阳,男,博士,副教授,研究方向为李代数与表示理论.E-mail:yiyang_li1979@aliyun.com.

收稿日期: 2017-04-17

  网络出版日期: 2018-05-29

基金资助

国家自然科学基金（11671138）；新疆维吾尔自治区自然科学基金（2016D01A014）

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Hom-spaces for subregular nilpotent representations of sl(n+1)

  • LI Yi-yang ,
  • SHU Bin ,
  • YE Gang
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  • 1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
    2. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China

Received date: 2017-04-17

  Online published: 2018-05-29

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摘要

令李代数g=sl（n+l）的基域是特征为素数p的代数闭域k且满足pn+1.本文在g的次正则幂零表示中，证明了相同块中的任意两个小Verma模的同态是非零的.这揭示了小Verma模之间的完整联系.

关键词： 标准Levi型; 小Verma模; 次正则幂零; 同态空间

本文引用格式

李宜阳 , 舒斌 , 叶刚 . sl(n+1)的次正则幂零表示的同态空间[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(3) : 18 -24,45 . DOI: 10.3969/j.issn.1000-5641.2018.03.002

Abstract

Let g=sl(n+1) be the special linear Lie algebra over an algebraically closed field k of prime characteristic p with pn+1. We show that the hom-spaces between any two baby Verma modules in the same given block are always nonzero for subregular nilpotent representations of g, which reveals a complete linkage atlas for baby Verma modules.

Key words： standard Levi-form; baby Verma module; subregular nilpotent; homspaces

参考文献

[1] KAC V, WEISFEILER B. Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristic p[J]. Indagationes Mathematicae, 1976, 38:136-151.
[2] FRIEDLANDER E M, PARSHALL B. Modular representation theory of Lie algebras[J]. The American Journal of Mathematics, 1988, 110:1055-1093.
[3] JANTZEN J C. Subregular nilpotent representations of sln and so2n+1[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1999, 126:223-257.
[4] JANTZEN J C. Representations of Lie algebras in prime characteristic[C]//Proceedings of Representation Theories and Algebraic Geometry. Montreal:NATO ASI, 1997.
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