Global theta lifting and automorphic periods associated to nilpotent orbits
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908465563172864 |
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| author | Jun, Bryan Wang Peng |
| author_facet | Jun, Bryan Wang Peng |
| contents | A systematic way to organise the interesting periods of automorphic forms on a reductive group $G$ is via the theory of nilpotent orbits of $G$. On the other hand, it is known that the theta correspondence can be used effectively to relate automorphic periods on each member of a dual pair. In this paper, we establish this relation in full generality, facilitated by a certain transfer of nilpotent orbits via moment maps. This is the analogous global result to the local result previously established by Gomez and Zhu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14234 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global theta lifting and automorphic periods associated to nilpotent orbits Jun, Bryan Wang Peng Number Theory Representation Theory 11F27, 11F70 A systematic way to organise the interesting periods of automorphic forms on a reductive group $G$ is via the theory of nilpotent orbits of $G$. On the other hand, it is known that the theta correspondence can be used effectively to relate automorphic periods on each member of a dual pair. In this paper, we establish this relation in full generality, facilitated by a certain transfer of nilpotent orbits via moment maps. This is the analogous global result to the local result previously established by Gomez and Zhu. |
| title | Global theta lifting and automorphic periods associated to nilpotent orbits |
| topic | Number Theory Representation Theory 11F27, 11F70 |
| url | https://arxiv.org/abs/2311.14234 |