Tilting sheaves for real groups and Koszul duality
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916951156064256 |
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| author | Ionov, Andrei Yun, Zhiwei |
| author_facet | Ionov, Andrei Yun, Zhiwei |
| contents | For a certain class of real analytic varieties with Lie group actions we develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, we construct a fully faithful embedding of the category of tilting sheaves to a real analog of the category of Soergel bimodules, establishing real group analogs of Soergel's Structure Theorem and Endomorphism Theorem. We apply these results to give a purely geometric proof of the theorem of Bezrukavnikov and Vilonen which proves Soergel's conjecture for quasi-split groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05409 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tilting sheaves for real groups and Koszul duality Ionov, Andrei Yun, Zhiwei Algebraic Geometry Representation Theory For a certain class of real analytic varieties with Lie group actions we develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, we construct a fully faithful embedding of the category of tilting sheaves to a real analog of the category of Soergel bimodules, establishing real group analogs of Soergel's Structure Theorem and Endomorphism Theorem. We apply these results to give a purely geometric proof of the theorem of Bezrukavnikov and Vilonen which proves Soergel's conjecture for quasi-split groups. |
| title | Tilting sheaves for real groups and Koszul duality |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2301.05409 |