An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914745831915520 |
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| author | Cho, Sungmun Lee, Yuchan |
| author_facet | Cho, Sungmun Lee, Yuchan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$ Cho, Sungmun Lee, Yuchan Number Theory Representation Theory 11F72, 11S80 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. |
| title | An explicit formula for the orbital integrals on the spherical Hecke algebra of $\mathrm{GL}_3$ |
| topic | Number Theory Representation Theory 11F72, 11S80 |
| url | https://arxiv.org/abs/2404.04666 |