Characters of the nullcone
Characters of the nullcone
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零锥体的特征
DOI：
10.1007/bf01420081
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发表时间：
1980
影响因子：
1.4
通讯作者：
W. Hesselink
中科院分区：
文献类型：
--
作者：
W. Hesselink
设G是~E上具有李代数9的半简单代数群。~的零元N由g的幂零元组成，它的坐标环A(N)是一个梯度环~ An(N)。我们在T的n>=0字符群P中固定了G的一个极大环面T和一个优势腔室C。如果2~ C设ez表示权值最高的不可约G模2。设d，(2)为E2在g模An(N)中的倍数。设R为根系。设R÷为正根的集合。放~:=1 / 2 ~ ~。如果z e P设P，(z)为映射f: R + ~ {O} u l N的个数，使得~tER + N =~f（~）和z=~f(~):~。设W为Weyl组。如果我们W，则设R(W): = R + n W R +和n(W): = #e R(W)和e（W): = (1) "tw）。我们证明下面的定理。
Let G be a semi-simple algebraic group over ~E with Lie algebra 9. The nullcone N of ~ consists of the nilpotent elements of g. Its co-ordinate ring A(N) is a graded ring ~ An(N ). We fix a maximal torus T of G and a dominant chamber C in the n>=0 character group P of T. If2~ C let E z denote the irreducible G-module with highest weight 2. Let d,(2) be the multiplicity of E2 in the G-module An(N ). Let R be the root system. Let R÷ be the set of the positive roots. Put ~:=1⁄2 ~ ~. If z e P let P,(Z) be the number of maps f : R + ~ { O } u l N such that ~tER + n= ~f (~) and z=~f(~):~. Let W be the Weyl group. If we W, put R(w) : = R + n w R + and n(w) : = #e R(w) and e(w) : = ( 1) "tw). We prove the following theorem.