IRREDUCIBLE REPRESENTATIONS OF LIE-ALGEBRAS OF REDUCTIVE GROUPS AND THE KAC-WEISFEILER CONJECTURE
成果类型：
Article
署名作者：
PREMET, A
署名单位：
University of California System; University of California Riverside
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/BF01884291
发表日期：
1995
页码：
79-117
关键词：
摘要：
Let g be the Lie algebra of a connected reductive group G over an algebraically closed field of characteristic p > 0. Suppose that G((1)) is simply connected and p is good for the root system of G. If p = 2, suppose in addition that g admits a nondegenerate G-invariant trace form. Let V be an irreducible and faithful g-module with p-character chi is an element of g*. It is proved in the paper that dim V is divisible by p(1/2dim Omega(chi)) where Omega(chi) stands for the orbit of chi under the coadjoint action of G.