On the $\mathrm{Sp}_{2n}$-distinguished automorphic spectrum of $\mathrm{U}_{2n}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929619690586112 |
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| author | Wang, Kewen Xin, Yu |
| author_facet | Wang, Kewen Xin, Yu |
| contents | Given a reductive group $G$ and a reductive subgroup $H$, both defined over a number field $F$, we introduce the notion of the $H$-distinguished automorphic spectrum of $G$ and analyze it for the pair $(\mathrm{U}_{2n},\mathrm{Sp}_{2n})$. We derived a formula for period integrals of pseudo-Eisenstein series of $\mathrm{U}_{2n}$ in analogy with the main result of Lapid and Offen in their work analyzing the pair $(\mathrm{Sp}_{4n},\mathrm{Sp}_{2n} \times \mathrm{Sp}_{2n})$. We give an upper bound of the distinguished spectrum with the formula. A non-trivial lower bound of the discrete distinguished spectrum is expected from the formula, given the previous work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $\mathrm{Sp}_{2n}$-distinguished automorphic spectrum of $\mathrm{U}_{2n}$ Wang, Kewen Xin, Yu Number Theory Representation Theory Given a reductive group $G$ and a reductive subgroup $H$, both defined over a number field $F$, we introduce the notion of the $H$-distinguished automorphic spectrum of $G$ and analyze it for the pair $(\mathrm{U}_{2n},\mathrm{Sp}_{2n})$. We derived a formula for period integrals of pseudo-Eisenstein series of $\mathrm{U}_{2n}$ in analogy with the main result of Lapid and Offen in their work analyzing the pair $(\mathrm{Sp}_{4n},\mathrm{Sp}_{2n} \times \mathrm{Sp}_{2n})$. We give an upper bound of the distinguished spectrum with the formula. A non-trivial lower bound of the discrete distinguished spectrum is expected from the formula, given the previous work. |
| title | On the $\mathrm{Sp}_{2n}$-distinguished automorphic spectrum of $\mathrm{U}_{2n}$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2412.05518 |