Asymptotics and local constancy of characters of p-adic groups

Ju-Lee Kim; Sug Woo Shin; Nicolas Templier

Asymptotics and local constancy of characters of p-adic groups

Representation Theory 2016-05-12 v2 Number Theory

Authors: Ju-Lee Kim , Sug Woo Shin , Nicolas Templier

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.

Keywords

p-adic groups representation theory trace character local constancy formal degree tame supercuspidal Moy-Prasad subgroups

Cite

@article{arxiv.1602.01758,
  title  = {Asymptotics and local constancy of characters of p-adic groups},
  author = {Ju-Lee Kim and Sug Woo Shin and Nicolas Templier},
  journal= {arXiv preprint arXiv:1602.01758},
  year   = {2016}
}

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Proceedings of Simons symposium on the trace formula

Asymptotics and local constancy of characters of p-adic groups

Abstract

Keywords

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