On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866917569901887488 |
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| author | Heyer, Claudius |
| author_facet | Heyer, Claudius |
| contents | We generalize a classical result of Andrianov on the decomposition of Hecke polynomials. Let $\mathfrak{F}$ be a non-archimedean local fied. For every connected reductive group $\mathbf{G}$, we give a criterion for when a polynomial with coefficients in the spherical parahoric Hecke algebra of $\mathbf{G}(\mathfrak{F})$ decomposes over a parabolic Hecke algebra associated with a non-obtuse parabolic subgroup of $\mathbf{G}$. We classify the non-obtuse parabolics. This then shows that our decomposition theorem covers all the classical cases due to Andrianov and Gritsenko. We also obtain new cases when the relative root system of $\mathbf{G}$ contains factors of types $E_6$ or $E_7$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2108_04535 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras Heyer, Claudius Number Theory 11C08, 20C08, 20G25 We generalize a classical result of Andrianov on the decomposition of Hecke polynomials. Let $\mathfrak{F}$ be a non-archimedean local fied. For every connected reductive group $\mathbf{G}$, we give a criterion for when a polynomial with coefficients in the spherical parahoric Hecke algebra of $\mathbf{G}(\mathfrak{F})$ decomposes over a parabolic Hecke algebra associated with a non-obtuse parabolic subgroup of $\mathbf{G}$. We classify the non-obtuse parabolics. This then shows that our decomposition theorem covers all the classical cases due to Andrianov and Gritsenko. We also obtain new cases when the relative root system of $\mathbf{G}$ contains factors of types $E_6$ or $E_7$. |
| title | On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras |
| topic | Number Theory 11C08, 20C08, 20G25 |
| url | https://arxiv.org/abs/2108.04535 |