On the K0 of a p-adic group
On the K0 of a p-adic group
复制标题
关于 p 进群的 K0
DOI：
10.1007/s002220050360
复制
发表时间：
2000
影响因子：
3.1
通讯作者：
Jean
中科院分区：
文献类型：
--
作者：
Jean
摘要。本文讨论了与Grothendieck群、不变分布、抛物和紧致归纳法有关的各种主题。主要的结果是用Levi子群的离散级数描述了Hecke代数h (G)的K0，它在抛物线约束和归纳法方面具有有趣的性质。得到了类似的描述，但与这些抛物型函子不相容
Abstract.This article deals with various topics related with Grothendieck groups, invariant distributions, parabolic and compact inductions... for a p-adic group G. The main result is a description of the K0 of the Hecke algebra ℋ of G in terms of discrete series of Levi subgroups, which has an interesting behavior with regard to parabolic restriction and induction. A similar description – but no more compatible with these parabolic functors – is obtained for
$\overline{\mathcal{H}}$=ℋ/[ℋ,ℋ] and the Hattori rank map gets an easy description in this dictionary.¶We follow a beautiful idea of J. Bernstein consisting in comparing two natural filtrations on these objects, one of combinatorial nature and one of topological nature. The combinatorial filtrations are related to the structure of Levi subgroupsin G and have counterparts concerning many classical objects of interest as the Grothendieck group of finite length G-modules R(G), the set Ωsr of regular semi-simple conjugacy classes, and the variety Θ(G) of infinitesimal characters. These filtrations will turn out to be “compatible”, in a sense to be specified, with regard to all the classical operations or morphisms between these objects.