Supercuspidal support of irreducible modulo l-representations of SL_n(F)

TL;DR

This paper proves the uniqueness of supercuspidal support for irreducible smooth modulo l representations of Levi subgroups of SL_n(F), extending understanding of their structure in characteristic l.

Contribution

It establishes the uniqueness of supercuspidal support for irreducible modulo l representations of Levi subgroups of SL_n(F), a result previously unknown in this setting.

Findings

Supercuspidal support is unique up to conjugation.

The result applies to both finite fields and non-archimedean local fields.

Supports the classification of mod l representations of SL_n(F).

Abstract

Let k be an algebraically closed field with characteristic l different from p. We show that the supercuspidal support of irreducible smooth k-representations of Levi subgroups M' of SL_n(F) is unique up to M'-conjugation, where F is either a finite field of characteristic p or a non-archimedean locally compact field of residual characteristic p.