The Wavefront Sets of Unipotent Supercuspidal Representations

TL;DR

This paper computes the wavefront sets of unipotent supercuspidal representations of semisimple p-adic groups, providing detailed algebraic and canonical classifications within Lusztig's framework.

Contribution

It introduces explicit calculations of wavefront sets for unipotent supercuspidal representations, advancing understanding of their structure in p-adic representation theory.

Findings

Computed algebraic wavefront sets for unipotent supercuspidal representations

Determined canonical unramified wavefront sets within Lusztig's category

Enhanced classification of supercuspidal representations based on wavefront data

Abstract

Let $\mathbf{G}(\mathsf{k})$ be a semisimple $p$-adic group, inner to split. In this article, we compute the algebraic and canonical unramified wavefront sets of the irreducible supercuspidal representations of $\mathbf{G}(\mathsf{k})$ in Lusztig's category of unipotent representations.