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arXiv · 2404.04666

An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$

Sungmun Cho·Yuchan Lee
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Abstract

We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in $\mathrm{GL}_n(F) \cap \mathrm{M}_n(\mathfrak{o})$ and associated with arbitrary elements of the spherical Hecke algebra of $\mathrm{GL}_n(F)$ when $n=2, 3$, using results of [CKL]. Here $F$ is a non-Archimedean local field of any characteristic with $\mathfrak{o}$ its ring of integers.

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Sungmun Cho, Yuchan Lee. 2024-04-06. An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$. https://arxiv.org/abs/2404.04666

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