Introduction to the relative Langlands program
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911168837189632 |
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| author | Beuzart-Plessis, Raphaël |
| author_facet | Beuzart-Plessis, Raphaël |
| contents | The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of Langlands functoriality and special values of (automorphic) $L$-functions. Following the work of Sakellaridis and Sakellaridis-Venkatesh, we emphasize the unifying role played by spherical varieties and harmonic analysis on them. We also review various instances of the phenomena, discovered by Jacquet, Gan-Gross-Prasad, Ichino-Ikeda and many others, that motivated these developments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introduction to the relative Langlands program Beuzart-Plessis, Raphaël Number Theory Representation Theory The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of Langlands functoriality and special values of (automorphic) $L$-functions. Following the work of Sakellaridis and Sakellaridis-Venkatesh, we emphasize the unifying role played by spherical varieties and harmonic analysis on them. We also review various instances of the phenomena, discovered by Jacquet, Gan-Gross-Prasad, Ichino-Ikeda and many others, that motivated these developments. |
| title | Introduction to the relative Langlands program |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2509.18062 |