仿射Weyl群族af_s(W)s∈R的结构

THE STRUCTION OF S-AFFINE WEYL GROUPS OF FINITE DIMENSION SIMPLE LIE ALGEBRA

本文给出有限维单李代数g( )的s-仿射Weyl群afs(W) (s∈R)的定义 ,讨论了这类变换群的结构性质 .并且证明了以下结论 : 对每个s∈R ,s-仿射Weyl群afs(W)同构于仿射型Kac -Moody代数g(A)的Weyl群W ; 对s∈Z ,afs(W)可由af1 (W)生成 . 对于每个λ∈η s 设Wλ 是λ在W中的稳定子群 ,则afs(Wλ)=(Wafs) λ, λ是λ在 η

In this present paper we define the s-affine Weyl group af _s(W) of finite dimensional simple complex Lie algebra g() when s is a real number; and prove that s-affine Weyl group is isomorphic to the Weyl group of affine Kac-Moody algebra g(A); and discuss the struction of s-affine Weyl groups, that is ,{W_(af _s)|s∈Z}=<W_(af _1)>