Affine Hecke algebras and their graded version
Affine Hecke algebras and their graded version
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DOI：
10.1090/s0894-0347-1989-0991016-9
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发表时间：
1989-09
影响因子：
3.9
通讯作者：
G. Lusztig
中科院分区：
文献类型：
--
作者：
G. Lusztig
0.1.设H，o是一个仿射Hecke代数，其参数v0 ∈ C* 为无穷级. (The对应于简单反射s的基元素Ts ∈ H，o满足（Ts +1）（Ts v2 c（s））= 0，其中C（S）∈ N依赖于s，并且只要s，s在仿射Weyl群中共轭，则仅服从c（s）= c（s '）。这样的Hecke代数自然出现在半单p-adic群的表示论中，理解它们的表示论是一个相当有趣的问题。考虑“特殊情况”，其中c（s）独立于s，并且coroot生成直接被加数。在这种“特殊情况”下，文[1]研究了上述问题，得到了单模的一个分类。[1]的方法是基于等变K-理论。这种方法可以在一般情况下尝试（在[5，0.3]中给出了一些指示），但在执行时似乎存在一些严重的困难。
0.1. Let H,o be an affine Hecke algebra with parameter v0 E C* assumed to be of infinite order. (The basis elements Ts E H,o corresponding to simple reflections s satisfy (Ts + l)(Ts v2c(s)) = 0, where C(S) E N depend on s and are subject only to c(s) = c(s') whenever s, s are conjugate in the affine Weyl group.) Such Hecke algebras appear naturally in the representation theory of semisimple p-adic groups, and understanding their representation theory is a question of considerable interest. Consider the "special case" where c(s) is independent of s and the coroots generate a direct summand. In this "special case," the question above has been studied in [1] and a classification of the simple modules was obtained. The approach of [1] was based on equivariant K-theory. This approach can be attempted in the general case (some indications are given in [5, 0.3]), but there appear to be some serious difficulties in carrying it out.