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The Generalized Restricted Representations of Graded Lie Algebras of Cartan Type

✍ Scribed by Bin Shu

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 363 KB
Volume: 194
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.7021

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✦ Synopsis

DEDICATED TO PROFESSOR GUANG-YU SHEN ON THE OCCASION OF HIS 65TH BIRTHDAY

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 Ž . Ž 2 . LsX m : n , X s W, S, H, or K, is a generalized restricted Lie algebra Ä 4 associated with a standard basis E of L and s a positive integer G max n .

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 . The descriptions of the blocks 1q ␦ ⑀ ,w 0x

X ,K m and a Brauer-type reciprocity are obtained.

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