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

TL;DR

This paper investigates the properties of admissible representations of reductive p-adic groups, demonstrating local constancy of characters and analyzing the growth of invariant subspaces using geometric methods.

Contribution

It introduces a geometric approach via coefficient systems on the Bruhat-Tits building to study characters and invariants of p-adic group representations, providing explicit neighborhoods of constancy.

Findings

Character function is locally constant.

Explicit neighborhoods of constancy are provided.

Growth estimates for invariant subspaces are derived.

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.