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Cocenters and representations of affine Hecke algebras. (English) Zbl 1373.20002

The elliptic representation of \(p\)-adic groups and associated affine Hecke algebras has been an active research area. The dual object is the so-called elliptic cocenter which is far from good understanding. In this paper, the authors introduce some notions of rigid quotients of the Grothendieck group of finite-dimensional representations and rigid cocenters of the affine Hecke algebras in order to understand the elliptic cocenter. They give bases for the rigid centers as well as the cocenters for the affine Hecke algebras, and some analogues to the density theorem and the trace Paley-Wiener theorem for affine Hecke algebras.
Reviewer: Hu Jun (Beijing)

MSC:

20C08 Hecke algebras and their representations
22E50 Representations of Lie and linear algebraic groups over local fields
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20E45 Conjugacy classes for groups
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