Theta correspondence and Springer correspondence
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912770486697984 |
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| author | Ma, Jia-Jun Qiu, Congling Yun, Zhiwei Zou, JiaLiang |
| author_facet | Ma, Jia-Jun Qiu, Congling Yun, Zhiwei Zou, JiaLiang |
| contents | In this paper, we obtain an explicit formula for the theta correspondence of unipotent principal-series representations between an even orthogonal and a symplectic group or between general linear groups over a finite field. The formula is in terms of the Springer correspondence. Along the way we prove general results about module categories of Hecke categories arising from spherical varieties, and give a similar formula for the multiplicities of the unipotent principal series representations in the function space of the spherical variety in terms of relative Springer theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theta correspondence and Springer correspondence Ma, Jia-Jun Qiu, Congling Yun, Zhiwei Zou, JiaLiang Representation Theory In this paper, we obtain an explicit formula for the theta correspondence of unipotent principal-series representations between an even orthogonal and a symplectic group or between general linear groups over a finite field. The formula is in terms of the Springer correspondence. Along the way we prove general results about module categories of Hecke categories arising from spherical varieties, and give a similar formula for the multiplicities of the unipotent principal series representations in the function space of the spherical variety in terms of relative Springer theory. |
| title | Theta correspondence and Springer correspondence |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2512.13020 |