Explicit asymptotic expansions in p-adic harmonic analysis II
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910006782197760 |
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| author | Spice, Loren |
| author_facet | Spice, Loren |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12935 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Explicit asymptotic expansions in p-adic harmonic analysis II Spice, Loren Representation Theory 22E50, 22E35 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. |
| title | Explicit asymptotic expansions in p-adic harmonic analysis II |
| topic | Representation Theory 22E50, 22E35 |
| url | https://arxiv.org/abs/2108.12935 |