Asymptotics and local constancy of characters of p-adic groups

Abstract

In this paper we study quantitative aspects of trace characters ${\Theta }_{\pi }$ of reductive $p$-adic groups when the representation $\pi$ 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 ${\Theta }_{\pi }$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.

arXiv commentProceedings of Simons symposium on the trace formula