A distinction criterion for Iwahori-spherical representations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910512952901632 |
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| author | Broussous, Paul |
| author_facet | Broussous, Paul |
| contents | Let $G/H$ be a Galois symmetric space for an unramified quadratic extension of a locally compact field $F$, where the group $H$ is semisimple, simply connected, defined and split over $F$. We prove that there exists a subgroup $Γ= Γ(G/H)$ of the group of invertible elements of the Iwahori-Hecke algebra $\mathcal H$ of $G$ such that an Iwahori-spherical representation of $G$ is $H$-distinguished if and only if the corresponding Iwahori-Hecke module is "$Γ$-distinguished". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A distinction criterion for Iwahori-spherical representations Broussous, Paul Representation Theory Let $G/H$ be a Galois symmetric space for an unramified quadratic extension of a locally compact field $F$, where the group $H$ is semisimple, simply connected, defined and split over $F$. We prove that there exists a subgroup $Γ= Γ(G/H)$ of the group of invertible elements of the Iwahori-Hecke algebra $\mathcal H$ of $G$ such that an Iwahori-spherical representation of $G$ is $H$-distinguished if and only if the corresponding Iwahori-Hecke module is "$Γ$-distinguished". |
| title | A distinction criterion for Iwahori-spherical representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2407.03714 |