A realization of irreducible representations of affine Weyl groups
A realization of irreducible representations of affine Weyl groups
复制标题
仿射Weyl群不可约表示的实现
DOI：
10.1016/1385-7258(83)90056-2
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发表时间：
1983
影响因子：
1.3
通讯作者：
S. Kato
中科院分区：
文献类型：
--
作者：
S. Kato
1.设G是C上的连通约化群，4(或gf)是G的包含GE的Bore1子群的簇。最近，Lusztig[6]利用DGM-扩张(中交上同调群[3])定义了G的上同调群W的表示。但是，正如后面将看到的，W的这些表示扩展到F_i的表示，即G的修正仿射Weyl群(I@的定义见第3节)。在这篇文章中，我们将说明如何分解上上同调中的@-表示，从而得到@的所有不可约表示(参看[5，9，
1. Let G be a connected reductive group over C and let 4 (or gf) be the variety of Bore1 subgroups of G which contain gE G. Recently, Lusztig [6] has defined representations of W, the Weyl group of G, on the cohomology groups of 4 by using DGM-extensions (middle intersection cohomology groups [3]). But, as will be seen later, these representations of W extend to those of fi, the modified affine Weyl group of G (see Section 3 for the definition of I@. In this paper, we shall show how to decompose the@-representation in the top cohomology, so that all irreducible representations of@ are obtained (cf.[5, 9,