Modulation groups
Fuente:
arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912755356794880 |
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| author | Getz, Jayce R. Terradillos, Armando Gutiérrez Hosseinijafari, Farid Hu, Bryan Lee, Seewoo Slipper, Aaron Tomé, Marie-Hélène Yao, HaoYun Zhao, Alan |
| author_facet | Getz, Jayce R. Terradillos, Armando Gutiérrez Hosseinijafari, Farid Hu, Bryan Lee, Seewoo Slipper, Aaron Tomé, Marie-Hélène Yao, HaoYun Zhao, Alan |
| contents | Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of a group that we christen the modulation group. This provides a broad generalization of the defining representation of the metaplectic group. The example of a vector space and the zero locus of a quadric cone in an even number of variables are discussed in detail. In both of these cases the modulation group is closely related to algebraic groups, and we propose a conjectural method of linking modulation groups to ind-algebraic groups in general. At the end of the paper we discuss adelization and the relationship between representations of modulation groups and the Poisson summation conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modulation groups Getz, Jayce R. Terradillos, Armando Gutiérrez Hosseinijafari, Farid Hu, Bryan Lee, Seewoo Slipper, Aaron Tomé, Marie-Hélène Yao, HaoYun Zhao, Alan Number Theory Algebraic Geometry Representation Theory 1F70, 11F27 Conjectures of Braverman and Kazhdan, Ngô and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of a group that we christen the modulation group. This provides a broad generalization of the defining representation of the metaplectic group. The example of a vector space and the zero locus of a quadric cone in an even number of variables are discussed in detail. In both of these cases the modulation group is closely related to algebraic groups, and we propose a conjectural method of linking modulation groups to ind-algebraic groups in general. At the end of the paper we discuss adelization and the relationship between representations of modulation groups and the Poisson summation conjecture. |
| title | Modulation groups |
| topic | Number Theory Algebraic Geometry Representation Theory 1F70, 11F27 |
| url | https://arxiv.org/abs/2510.23932 |