Godement--Jacquet L-function and homological theta lifting
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916836878057472 |
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| author | Chen, Rui Li, Yufeng Long, Xiaohuan Tang, Chenhao Zou, Jialiang |
| author_facet | Chen, Rui Li, Yufeng Long, Xiaohuan Tang, Chenhao Zou, Jialiang |
| contents | In this paper we investigate the theta lifting of type II dual pairs over a non-Archimedean local field, by combining the homological method of Adams--Prasad--Savin and the analytic method of Fang--Sun--Xue. We have three main results: 1. we determine completely the big theta lift of an irreducible representation when its Godement--Jacquet L-function is holomorphic at a critical point; 2. we compute the big theta lift of all characters, hence determine the space of eigendistributions on matrix spaces for all characters; 3. we show that the Weil representation is projective if and only if the dual pair is almost in the stable range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Godement--Jacquet L-function and homological theta lifting Chen, Rui Li, Yufeng Long, Xiaohuan Tang, Chenhao Zou, Jialiang Representation Theory Number Theory In this paper we investigate the theta lifting of type II dual pairs over a non-Archimedean local field, by combining the homological method of Adams--Prasad--Savin and the analytic method of Fang--Sun--Xue. We have three main results: 1. we determine completely the big theta lift of an irreducible representation when its Godement--Jacquet L-function is holomorphic at a critical point; 2. we compute the big theta lift of all characters, hence determine the space of eigendistributions on matrix spaces for all characters; 3. we show that the Weil representation is projective if and only if the dual pair is almost in the stable range. |
| title | Godement--Jacquet L-function and homological theta lifting |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2507.07531 |