Schubert Eisenstein series and Poisson summation for Schubert varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916482817982464 |
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| author | Choie, YoungJu Getz, Jayce R. |
| author_facet | Choie, YoungJu Getz, Jayce R. |
| contents | The first author and Bump defined Schubert Eisenstein series by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of $\mathrm{GL}_3$ over $\mathbb{Q}$ they proved that these Schubert Eisenstein series have meromorphic continuations in all parameters and conjectured the same is true in general. We revisit their conjecture and relate it to the program of Braverman, Kazhdan, Lafforgue, Ngô, and Sakellaridis aimed at establishing generalizations of the Poisson summation formula. We prove the Poisson summation formula for certain schemes closely related to Schubert varieties and use it to refine and establish the conjecture of the first author and Bump in many cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_01874 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Schubert Eisenstein series and Poisson summation for Schubert varieties Choie, YoungJu Getz, Jayce R. Number Theory Representation Theory 11F70 (Primary) 11F55, 11F85 (Secondary) The first author and Bump defined Schubert Eisenstein series by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of $\mathrm{GL}_3$ over $\mathbb{Q}$ they proved that these Schubert Eisenstein series have meromorphic continuations in all parameters and conjectured the same is true in general. We revisit their conjecture and relate it to the program of Braverman, Kazhdan, Lafforgue, Ngô, and Sakellaridis aimed at establishing generalizations of the Poisson summation formula. We prove the Poisson summation formula for certain schemes closely related to Schubert varieties and use it to refine and establish the conjecture of the first author and Bump in many cases. |
| title | Schubert Eisenstein series and Poisson summation for Schubert varieties |
| topic | Number Theory Representation Theory 11F70 (Primary) 11F55, 11F85 (Secondary) |
| url | https://arxiv.org/abs/2107.01874 |