Generalised Whittaker models as instances of relative Langlands duality
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909704748269568 |
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| author | Gan, Wee Teck Jun, Bryan Wang Peng |
| author_facet | Gan, Wee Teck Jun, Bryan Wang Peng |
| contents | The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a duality theory of branching problems. This often unexpectedly relates two a priori unrelated branching problems. We examine how the generalised Whittaker (or Gelfand-Graev) models serve as the prototypical example for such branching problems. We give a characterization, for the orthogonal and symplectic groups, of the generalised Whittaker models possibly contained in this duality theory. We then exhibit an infinite family of examples of this duality, which, provably at the local level via the theta correspondence, satisfy the conjectural expectations of duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08874 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalised Whittaker models as instances of relative Langlands duality Gan, Wee Teck Jun, Bryan Wang Peng Representation Theory Number Theory Symplectic Geometry 22E50, 53D50 The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a duality theory of branching problems. This often unexpectedly relates two a priori unrelated branching problems. We examine how the generalised Whittaker (or Gelfand-Graev) models serve as the prototypical example for such branching problems. We give a characterization, for the orthogonal and symplectic groups, of the generalised Whittaker models possibly contained in this duality theory. We then exhibit an infinite family of examples of this duality, which, provably at the local level via the theta correspondence, satisfy the conjectural expectations of duality. |
| title | Generalised Whittaker models as instances of relative Langlands duality |
| topic | Representation Theory Number Theory Symplectic Geometry 22E50, 53D50 |
| url | https://arxiv.org/abs/2309.08874 |