On families of degenerate representations of GL_n(F)
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910902459039744 |
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| author | Girsch, Johannes Helm, David |
| author_facet | Girsch, Johannes Helm, David |
| contents | We consider the stratification of the category of smooth representations of $\mbox{GL}_n(F)$ (for $F$ a $p$-adic field) induced by degenerate Whittaker models. We show that, remarkably, the successive quotient categories in this stratification turn out to be module categories over commutative rings. In fact these rings turn out to be infinite products of smooth algebras over the ground field. We further obtain explict descriptions of these rings in terms of the Zelevinsky classification; these descriptions closely resemble the Bernstein-Deligne description of the Bernstein center. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On families of degenerate representations of GL_n(F) Girsch, Johannes Helm, David Representation Theory Number Theory 11F70, 22E50 We consider the stratification of the category of smooth representations of $\mbox{GL}_n(F)$ (for $F$ a $p$-adic field) induced by degenerate Whittaker models. We show that, remarkably, the successive quotient categories in this stratification turn out to be module categories over commutative rings. In fact these rings turn out to be infinite products of smooth algebras over the ground field. We further obtain explict descriptions of these rings in terms of the Zelevinsky classification; these descriptions closely resemble the Bernstein-Deligne description of the Bernstein center. |
| title | On families of degenerate representations of GL_n(F) |
| topic | Representation Theory Number Theory 11F70, 22E50 |
| url | https://arxiv.org/abs/2504.02098 |