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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.10635 |
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| _version_ | 1866912072533540864 |
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| author | Friedberg, Solomon Ginzburg, David Offen, Omer |
| author_facet | Friedberg, Solomon Ginzburg, David Offen, Omer |
| contents | We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible component of the residual spectrum of the rank $k$ symplectic group $\mathrm{Sp}_k$ for any $k\ge 2n$. We show that this residual representation admits a non-zero $\mathrm{Sp}_n\times \mathrm{Sp}_{k-n}$-invariant linear form. This generalizes a construction of Ginzburg, Rallis and Soudry, the case $k=2n$, that arises in the descent method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On residual automorphic representations and period integrals for symplectic groups Friedberg, Solomon Ginzburg, David Offen, Omer Number Theory Representation Theory We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible component of the residual spectrum of the rank $k$ symplectic group $\mathrm{Sp}_k$ for any $k\ge 2n$. We show that this residual representation admits a non-zero $\mathrm{Sp}_n\times \mathrm{Sp}_{k-n}$-invariant linear form. This generalizes a construction of Ginzburg, Rallis and Soudry, the case $k=2n$, that arises in the descent method. |
| title | On residual automorphic representations and period integrals for symplectic groups |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2410.10635 |