Shallow Characters and Supercuspidal Representations

2020/10/30 by Gastineau, Stella Sue
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2011.00049

Abstract

In 2014, Reeder and Yu constructed epipelagic representations of a reductive p-adic group G from stable functions on shallowest Moy-Prasad quotients. In this paper, we extend these methods when G is split. In particular, we classify all complex-valued characters vanshing on a slightly deeper Moy-Prasad subgroup and show that, while sufficient, a naive extension of Reeder-Yu's stability condition is not necessary for constructing supercuspidal representations.

Related

• Supercuspidal representations: construction, classification, and characters
• Distinguished regular supercuspidal representations
• Représentations supercuspidales
• Regular supercuspidal representations
• Supercuspidal representations: an exhaustion theorem