Universal Koszul Duality for Kac-Moody Groups
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908615565115392 |
|---|---|
| author | Eberhardt, Jens Niklas Eteve, Arnaud |
| author_facet | Eberhardt, Jens Niklas Eteve, Arnaud |
| contents | We prove a monoidal equivalence, called universal Koszul duality, between genuine equivariant K-motives on a Kac-Moody flag variety and constructible monodromic sheaves on its Langlands dual. The equivalence is obtained by a Soergel-theoretic description of both sides which extends results for finite-dimensional flag varieties by Taylor and the first author.
Universal Koszul duality bundles together a whole family of equivalences for each point of a maximal torus. At the identity, it recovers an ungraded version of Beilinson-Ginzburg-Soergel's and Bezrukavnikov-Yun's Koszul duality for equivariant and unipotently monodromic sheaves. It also generalizes Soergel-theoretic descriptions for monodromic categories on finite-dimensional flag varieties by Lusztig-Yun, Gouttard and the second author. For affine Kac-Moody groups, our work sheds new light on the conjectured quantum Satake equivalences by Cautis-Kamnitzer and Gaitsgory.
On our way, we establish foundations on six functors for reduced K-motives and introduce a formalism of constructible monodromic sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Koszul Duality for Kac-Moody Groups Eberhardt, Jens Niklas Eteve, Arnaud Representation Theory Algebraic Geometry K-Theory and Homology We prove a monoidal equivalence, called universal Koszul duality, between genuine equivariant K-motives on a Kac-Moody flag variety and constructible monodromic sheaves on its Langlands dual. The equivalence is obtained by a Soergel-theoretic description of both sides which extends results for finite-dimensional flag varieties by Taylor and the first author. Universal Koszul duality bundles together a whole family of equivalences for each point of a maximal torus. At the identity, it recovers an ungraded version of Beilinson-Ginzburg-Soergel's and Bezrukavnikov-Yun's Koszul duality for equivariant and unipotently monodromic sheaves. It also generalizes Soergel-theoretic descriptions for monodromic categories on finite-dimensional flag varieties by Lusztig-Yun, Gouttard and the second author. For affine Kac-Moody groups, our work sheds new light on the conjectured quantum Satake equivalences by Cautis-Kamnitzer and Gaitsgory. On our way, we establish foundations on six functors for reduced K-motives and introduce a formalism of constructible monodromic sheaves. |
| title | Universal Koszul Duality for Kac-Moody Groups |
| topic | Representation Theory Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2408.14716 |