Conformal limits in Cayley components and $Θ$-positive opers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911984199401472 |
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| author | Kydonakis, Georgios Yang, Mengxue |
| author_facet | Kydonakis, Georgios Yang, Mengxue |
| contents | We study Gaiotto's conformal limit for the $G^{\mathbb{R}}$-Hitchin equations, when $G^{\mathbb{R}}$ is a simple real Lie group admitting a $Θ$-positive structure. We identify a family of flat connections coming from certain solutions to the equations for which the conformal limit exists and admits the structure of an oper. We call this new class of opers appearing in the conformal limit $Θ$-positive opers. The two families involved are parameterized by the same base space. This space is a generalization of the base of Hitchin's integrable system in the case when the structure group is a split real group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal limits in Cayley components and $Θ$-positive opers Kydonakis, Georgios Yang, Mengxue Differential Geometry Algebraic Geometry Quantum Algebra Primary: 58E15, 53C07, 22E15. Secondary: 14D21, 81T13 We study Gaiotto's conformal limit for the $G^{\mathbb{R}}$-Hitchin equations, when $G^{\mathbb{R}}$ is a simple real Lie group admitting a $Θ$-positive structure. We identify a family of flat connections coming from certain solutions to the equations for which the conformal limit exists and admits the structure of an oper. We call this new class of opers appearing in the conformal limit $Θ$-positive opers. The two families involved are parameterized by the same base space. This space is a generalization of the base of Hitchin's integrable system in the case when the structure group is a split real group. |
| title | Conformal limits in Cayley components and $Θ$-positive opers |
| topic | Differential Geometry Algebraic Geometry Quantum Algebra Primary: 58E15, 53C07, 22E15. Secondary: 14D21, 81T13 |
| url | https://arxiv.org/abs/2408.06198 |