阶化Cartan型代数S(m；n)的不可约表示及其约化  

Irreducible Representations of Graded Cartan Type Algebra S(m;n) and Reduction

作　　者：姚裕丰[1] 舒斌[1] 

机构地区：[1]华东师范大学数学系,上海200241

出　　处：《数学年刊（A辑）》2008年第6期859-872,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10871067);上海市基础数学重点基金资助的项目.

摘　　要：设L=S(m;n)是定义在特征p>3的代数闭合域F上的阶化特殊型李代数,利用已研究L的不可约表示的方法,通过定义L的如下阶化:限制情形定义L=(?)L_([q],I),非限制情形定义L=(?)L_([q],I),这里L是L的本原p-包络,有表达式L=L (?) sum from i=1 to m sum from (d_i=1)to (n_i-1) FD_i^(P^(d_i)),而I是{1、2,…,m}的子集,得到当p-特征标χ是正则半单时,在限制李代数情形所有不可约L_χ(L)-模都是从不可约U_χ(L_([0],I))-模诱导的;在非限制的情形,所有不可约U_(?)(U_(p^s)(L,χ))-模都是从不可约U_(?)(L_([0],I))-模诱导的,这里(?)是χ到L~*上的平凡扩张.Let L = S（m; n） be a graded special algebra over an algebraically closed field F of characteristic p 〉 3. This paper uses the methods developed by Shu Bin to study irreducible representations of L. With aid of the gradation structure of L = S（m; 1） defined via L = q≥-1 L[q], I for restricted case, and L = q≥-1L[q], I for non-restricted case, where L=Li=1 m∑i=1 ni-1∑di=1FDpdii is the canonical primitive p-envelope of L, and I is a subset of{1,2,… ,m}, It is proved that when the character X is regular semisimple, each simple Ux（L）-module is induced from a simple Ux（L[0], 1）-module for restricted case; each simple U-x（L）（Upn（L,x））-module is induced from a simple U-x（L[0], 1）-module for non-restricted case.Here X- is a trivial extension of x to L＊.

关 键 词：阶化Caftan型李代数 特殊代数 广义限制李代数 广义限制表示 p-特征标 

分 类 号：O152.5[理学—数学]