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arXiv · 1602.01758

Asymptotics and local constancy of characters of p-adic groups

Ju-Lee Kim·Sug Woo Shin·Nicolas Templier
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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.

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Ju-Lee Kim, Sug Woo Shin, Nicolas Templier. 2016-05-10. Asymptotics and local constancy of characters of p-adic groups. https://arxiv.org/abs/1602.01758

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