Restricting admissible representations to fixed-point subgroups

2021/04/04 by Latham, Peter, Nevins, Monica
#22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2104.01510

Abstract

Given a p-adic group G equipped with an action of a finite group Γ\subsetAut_F(G), and a reductive fixed-point subgroup G^Γ, we establish a relationship between constructions of types for these two groups due to Yu, Kim--Yu and Fintzen, and generalizes the relationship between general linear and classical groups observed by Stevens. As an application, given a parabolically induced or supercuspidal representation π of G, we explicitly identify a number of the inertial equivalence classes occurring in the representation π|_G^[Γ].

Related

• Supercuspidal representations in non-defining characteristics
• Some results on the admissible representations of non-connected reductive p-adic groups
• Some questions about representations of p-adic groups
• Geometric structure in the representation theory of p-adic groups
• Supercuspidal representations: an exhaustion theorem