Asymptotics and local constancy of characters of p-adic groups

2016/02/04 by Kim, Ju-Lee, Shin, Sug Woo, Templier, Nicolas
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1602.01758

Abstract

In this paper we study quantitative aspects of trace characters Θ_π of reductive p-adic groups when the representation π varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of Θ_π relative to the formal degree of π, which we are able to prove in the case where π is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.

Related

• Uniform bounds on the Harish-Chandra characters
• On the local constancy of characters
• Characters of locally analytic representations of p-adic reductive groups
• Local Summability of Characters on p-adic Reductive Groups
• Regular supercuspidal representations