The Generalized Restricted Representations of Graded Lie Algebras of Cartan Type
The Generalized Restricted Representations of Graded Lie Algebras of Cartan Type
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DOI：
10.1006/jabr.1996.7021
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发表时间：
1997-08
影响因子：
0.9
通讯作者：
B. Shu
中科院分区：
文献类型：
--
作者：
B. Shu
摘要 设F为特征p > 2的代数闭域。本文介绍了广义限制李代数的概念及其在F上的广义限制表示。嘉当类型的任何分级李代数 L = X ( m : n ) (2) 、 X = W 、 S 、 H 或 K 是与 L 的标准基 E 相关联的广义受限李代数，并且 s 是一个正整数 ≥ max 1 ≤ i ≤ m { ni }。确定了L的不可约广义限制表示，与p sd 权函数一一对应；这里 d 是 L 1 + δ X , Ke m , [0] 中标准环面的尺寸。获得了块的描述和布劳尔型互易性。
Abstract Let F be an algebraically closed field of characteristic p > 2. In this paper, the concepts of generalized restricted Lie algebras and their generalized restricted representations over F are introduced. Any graded Lie algebra of Cartan type L = X ( m : n ) (2) , X = W , S , H , or K , is a generalized restricted Lie algebra associated with a standard basis E of L and s a positive integer ≥ max 1 ≤ i ≤ m { n i }. The irreducible generalized restricted representations of L are determined, which are in a one-to-one correspondence with p sd weight functions; here d is the dimension of the standard torus in L 1 + δ X , K e m , [0] . The descriptions of the blocks and a Brauer-type reciprocity are obtained.