On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field

TL;DR

This paper establishes an upper bound on the support of matrix coefficients for supercuspidal representations of GL(n) over non-archimedean local fields, providing an independent proof aligned with existing classification results.

Contribution

It offers a new, independent proof of support bounds for matrix coefficients of supercuspidal representations, complementing known classification-based approaches.

Findings

Upper bound on matrix coefficient support established

Results align with Bushnell–Kutzko classification

Proof provided independently of existing classification methods

Abstract

We derive an upper bound on the support of matrix coefficients of suprecuspidal representations of the general linear group over a non-archimedean local field. The results are in par with those which can be obtained from the Bushnell--Kutzko classification of supercuspidal representations, but they are proved independently.