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<p>We unwind the induction implicit in the “one-step” asymptotic expansions of (the author in Compositio Mathematica 154(11):2305–2378, <CitationRef CitationID="CR57">2018</CitationRef>) 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.</p>

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Explicit asymptotic expansions in \(p\)-adic harmonic analysis II

  • 期刊论文

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  • 发表日期：

    2026年3月23日

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  • Loren Spice

摘要

We unwind the induction implicit in the “one-step” asymptotic expansions of (the author in Compositio Mathematica 154(11):2305–2378, 2018) 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.