Geometric Langlands for Irregular Theta Connections and Epipelagic Representations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913537007288320 |
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| author | Chen, Tsao-Hsien Yi, Lingfei |
| author_facet | Chen, Tsao-Hsien Yi, Lingfei |
| contents | From a stable vector of a stable grading on a simple Lie algebra, Yun defined a rigid automorphic datum that encodes a epipelagic representation, and also an irregular connection on the projective line called $θ$-connection. We show that under geometric Langlands correspondence, $θ$-connection corresponds to the Hecke eigensheaf attached the rigid automorphic datum, assuming the stable grading is inner and its Kac coordinate $s_0$ is positive. We provide numerous applications of the main result including physical and cohomological rigidity of $θ$-connections, global oper structures, and a de Rham analog of Reeder-Yu's predictions on epipelagic Langlands parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Langlands for Irregular Theta Connections and Epipelagic Representations Chen, Tsao-Hsien Yi, Lingfei Representation Theory Algebraic Geometry From a stable vector of a stable grading on a simple Lie algebra, Yun defined a rigid automorphic datum that encodes a epipelagic representation, and also an irregular connection on the projective line called $θ$-connection. We show that under geometric Langlands correspondence, $θ$-connection corresponds to the Hecke eigensheaf attached the rigid automorphic datum, assuming the stable grading is inner and its Kac coordinate $s_0$ is positive. We provide numerous applications of the main result including physical and cohomological rigidity of $θ$-connections, global oper structures, and a de Rham analog of Reeder-Yu's predictions on epipelagic Langlands parameters. |
| title | Geometric Langlands for Irregular Theta Connections and Epipelagic Representations |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2407.20593 |