Effective results in representation theory of reductive groups over local fields

Abstract

We prove effective versions of several classical results in representation theory of reductive groups over non-Archimedean local fields of arbitrary characteristic. More specifically, we deal with the support of matrix coefficients of cuspidal representations and the recursions satisfied by matrix coefficients of representations of finite length. We provide effective generation results for irreducible representations. Finally, we study the effective smoothness of characters on the set of regular semi-simple elements.