Explicit asymptotic expansions in p-adic harmonic analysis II

2021/08/29 by Spice, Loren · 5 citations
#22E35 #22E50 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2108.12935

Abstract

We unwind the induction implicit in the "one-step" asymptotic expansions of arXiv:1701.02417 to describe how to turn asymptotic expansions, such as (but not limited to) the Harish-Chandra--Howe local character expansion, for depth-(0) supercuspidal characters into Kim--Murnaghan-type asymptotic expansions for arbitrary positive-depth, tame, supercuspidal characters. Doing so requires analogous results for Fourier transforms of orbital integrals on the Lie algebra of a reductive group, which are of independent interest.

Cited by

• Local character expansion for mod-ℓ representations
• Local characters of mod-ℓ representations of a p-adic reductive group
• Supercuspidal representations: construction, classification, and characters
• An introduction to representations of p-adic groups
• Langlands parameters for Moy-Prasad types

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