On the geometric Satake equivalence for Kac-Moody groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908604111519744 |
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| author | Bouthier, Alexis Vasserot, Eric |
| author_facet | Bouthier, Alexis Vasserot, Eric |
| contents | This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double affine grassmannian \Gr_{G}, seen as a infty-stack, that we equip with a t-structure. We obtain an Braden's hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact using dimension estimates for affine MV-cycles. We then deduce the sought-for equivalence and prove that the IC-complexes match with the irreducible highest weight representations of the Langlands dual group G^{\vee}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometric Satake equivalence for Kac-Moody groups Bouthier, Alexis Vasserot, Eric Representation Theory Mathematical Physics Algebraic Geometry This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double affine grassmannian \Gr_{G}, seen as a infty-stack, that we equip with a t-structure. We obtain an Braden's hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact using dimension estimates for affine MV-cycles. We then deduce the sought-for equivalence and prove that the IC-complexes match with the irreducible highest weight representations of the Langlands dual group G^{\vee}. |
| title | On the geometric Satake equivalence for Kac-Moody groups |
| topic | Representation Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2510.11466 |