A New Multiplicity Formula for the Weyl Modules of Type B and C  

作　　者：Jia Chen YE Ben Sheng YUN Jia ZHAN 

机构地区：[1]Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2010年第4期675-686,共12页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10671142)

摘　　要：A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.

关 键 词：simple Lie algebra multiplicity formula WEIGHT irreducible module. 

分 类 号：O152.6[理学—数学]