Parabolic geometric Eisenstein series and constant term functors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912506778222592 |
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| author | Faergeman, Joakim Hayash, Andreas |
| author_facet | Faergeman, Joakim Hayash, Andreas |
| contents | We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we establish various Hecke structures on geometric Eisenstein series functors, generalizing results of Braverman-Gaitsgory in the case of a principal parabolic. Moreover, we relate compactified and non-compactified geometric Eisenstein series functors via Koszul duality.
We sketch a proof that the spectral-to-automorphic geometric Langlands functor commutes with constant term functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic geometric Eisenstein series and constant term functors Faergeman, Joakim Hayash, Andreas Representation Theory Algebraic Geometry We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we establish various Hecke structures on geometric Eisenstein series functors, generalizing results of Braverman-Gaitsgory in the case of a principal parabolic. Moreover, we relate compactified and non-compactified geometric Eisenstein series functors via Koszul duality. We sketch a proof that the spectral-to-automorphic geometric Langlands functor commutes with constant term functors. |
| title | Parabolic geometric Eisenstein series and constant term functors |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2507.13930 |