Triality and Functoriality
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911279532212224 |
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| author | Chenevier, Gaëtan Gan, Wee Teck |
| author_facet | Chenevier, Gaëtan Gan, Wee Teck |
| contents | We use the triality automorphism of simple algebraic groups of type $D_4$ to prove some new instances of global Langlands functorial lifting. In particular, we prove the (weak) spin lifting from ${\rm GSp}_6$ to ${\rm GL}_8$ and the tensor product lifting from ${\rm GL}_2 \times {\rm GSp}_4$ to ${\rm GL}_8$. As an arithmetic application, we establish the expected properties of the spinor L-function attached to an arbitrary Siegel modular cusp form for ${\rm Sp}_6(\mathbb{Z})$ generating a holomorphic discrete series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triality and Functoriality Chenevier, Gaëtan Gan, Wee Teck Number Theory Representation Theory 11F27, 11F46, 11F55, 11F66, 11F70, 11F80, 11R39, 20G41, 20E50, 20E55 We use the triality automorphism of simple algebraic groups of type $D_4$ to prove some new instances of global Langlands functorial lifting. In particular, we prove the (weak) spin lifting from ${\rm GSp}_6$ to ${\rm GL}_8$ and the tensor product lifting from ${\rm GL}_2 \times {\rm GSp}_4$ to ${\rm GL}_8$. As an arithmetic application, we establish the expected properties of the spinor L-function attached to an arbitrary Siegel modular cusp form for ${\rm Sp}_6(\mathbb{Z})$ generating a holomorphic discrete series. |
| title | Triality and Functoriality |
| topic | Number Theory Representation Theory 11F27, 11F46, 11F55, 11F66, 11F70, 11F80, 11R39, 20G41, 20E50, 20E55 |
| url | https://arxiv.org/abs/2510.21169 |