Characters and growth of admissible representations of reductive p-adic groups

Abstract

We use coefficient systems on the affine Bruhat-Tits building to study admissible representations of reductive p-adic groups in characteristic not equal to p. We show that the character function is locally constant and provide explicit neighbourhoods of constancy. We estimate the growth of the subspaces of invariants for compact open subgroups.

Changes in the third version: the proof of Theorem 7.2 contained some mistakes. We repaired it, but to make it work we had to adjust Definition 7.1 a little

References in corpus (1)

• A character formula for compact elements (the rank one case)

Cited by in corpus (7)

• Caractères tordus des représentations admissibles
• Typical representations via fixed point sets in Bruhat--Tits buildings
• Cocenters of $p$-adic groups, III: Elliptic and rigid cocenters
• Local Summability of Characters on $p$-adic Reductive Groups
• Resolutions of tempered representations of reductive p-adic groups
• A characterization of groups of parahoric type
• Endoscopy and cohomology of U(n,1)