Characters of locally analytic representations of p-adic reductive groups

TL;DR

This paper introduces a new definition of characters for locally analytic representations of p-adic reductive groups, focusing on functions on compact subgroups of maximal tori, with an example involving SL(2,Q_p).

Contribution

It proposes a novel character theory within Schneider-Teitelbaum's framework, extending the understanding of locally analytic representations of p-adic groups.

Findings

Defined characters as functions on compact subgroups of maximal tori.

Applied the theory to locally analytic principal series of SL(2,Q_p).

Provided explicit examples illustrating the new character concept.

Abstract

We propose a definition of characters in the context of Schneider-Teitelbaum's theory of locally analytic representations of p-adic reductive groups. This character will be a function on a compact subgroup of a maximal torus of the reductive group in question. As an example we treat the locally analytic principal series of SL(2,Q_p).