Reduction to real infinitesimal character in affine Hecke algebras
Reduction to real infinitesimal character in affine Hecke algebras
复制标题
仿射赫克代数中的实无穷小特征的简化
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
A. Moy
中科院分区：
文献类型：
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作者：
D. Barbasch;A. Moy
本文的主要结果是证明了分裂p-adic群的非分歧酉对偶的判定问题等价于相应分次Hecke代数的酉对偶的判定问题。在[BM]中，作者在一定的限制下建立了岩堀球面表示的这种等价性;即，无穷小的特征必须是真实的（在[BMJ]的术语中）。对于Langlands-Deligne-Lusztig参数（s，u，p）[KUL]，限制条件是SELG是纯双曲元.在[BM]中使用的技术是将[V]中K-字符的签名的概念与[KL]中的一些事实相结合，即，回火表示的2 w-字符是线性独立的。当无穷小特征是真实的时，这基本上是正确的;因为如果不是，s有一个椭圆部分Se，使得
The main result of this paper is to show that the problem of the determination of the unramified unitary dual of a split p-adic group is equivalent to the problem of determining the unitary dual of the corresponding graded Hecke algebra. In [BM], the authors established this equivalence in the case of Iwahori spherical representations under a certain restriction; namely, it was essential for the infinitesimal character to be real (in the terminology of [BMJ). In terms of the Langlands-Deligne-Lusztig parameters (s, u, p) [KUL, the restriction is that S E LG be a purely hyperbolic element. The technique used in [BM] was to combine the notion of the signature of a K-character in [V] with some facts which follow from [KL], namely, that the 2w-characters of tempered representations are linearly independent. This is essentially true precisely when the infinitesimal character is real; for if not, s has an elliptic part Se such that