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arXiv · 2207.11296

Computations of orbital integrals and Shalika germs

Cheng-Chiang Tsai
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Abstract

For a reductive group $G$ over a non-archimedean local field, with some assumptions on (residue) characteristic we give an method to compute certain orbital integrals using a method close to that of Goresky-Kottiwitz-MacPherson but in a different language. These orbital integrals allow us to compute the Shalika germs at some ``very elliptic'' elements in terms of number of rational points on some quasi-finite covers of the Hessenberg varieties of GKM, which are subvarieties of (partial) flag varieties. Such values of Shalika germs determine the Harish-Chandra local character expansions of the so-called very supercuspidal representations.

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Cheng-Chiang Tsai. 2022-07-22. Computations of orbital integrals and Shalika germs. https://arxiv.org/abs/2207.11296

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