Multiplicative Hitchin fibrations and Langlands duality
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912591374188544 |
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| author | Gallego, Guillermo |
| author_facet | Gallego, Guillermo |
| contents | We identify pairs of (twisted) multiplicative Hitchin fibrations which are "dual" in the sense that their bases are identified and their generic fibres are dual Beilinson $1$-motives. More precisely, we match the following: (1) an untwisted multiplicative Hitchin fibration associated with a simply-laced semisimple group $G$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $G^\vee$; (2) a twisted multiplicative Hitchin fibration associated with a simply-laced and simply-connected semisimple group $G$, without factors of type $\mathsf{A}_{2\ell}$, and a diagram automorphism $θ\in \mathrm{Aut}(G)$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $H^\vee$ of the invariant group $H=G^θ$; (3) two twisted multiplicative Hitchin fibrations associated with $G=\mathrm{SL}_{2\ell +1}$ and two special automophisms of order $2$ and $4$, respectively. These results are consistent with a conjecture of Elliott and Pestun (arXiv:1812.05516). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicative Hitchin fibrations and Langlands duality Gallego, Guillermo Algebraic Geometry High Energy Physics - Theory Mathematical Physics 14D23, 14D24 We identify pairs of (twisted) multiplicative Hitchin fibrations which are "dual" in the sense that their bases are identified and their generic fibres are dual Beilinson $1$-motives. More precisely, we match the following: (1) an untwisted multiplicative Hitchin fibration associated with a simply-laced semisimple group $G$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $G^\vee$; (2) a twisted multiplicative Hitchin fibration associated with a simply-laced and simply-connected semisimple group $G$, without factors of type $\mathsf{A}_{2\ell}$, and a diagram automorphism $θ\in \mathrm{Aut}(G)$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $H^\vee$ of the invariant group $H=G^θ$; (3) two twisted multiplicative Hitchin fibrations associated with $G=\mathrm{SL}_{2\ell +1}$ and two special automophisms of order $2$ and $4$, respectively. These results are consistent with a conjecture of Elliott and Pestun (arXiv:1812.05516). |
| title | Multiplicative Hitchin fibrations and Langlands duality |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics 14D23, 14D24 |
| url | https://arxiv.org/abs/2509.14364 |