An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.04666
- arXiv:
- arXiv:2404.04666
- Bibcode:
- 2024arXiv240404666C
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Representation Theory;
- 11F72;
- 11S80
- E-Print:
- 17 pages