2026-09-21T16:01:57Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1446482022-08-30T03:49:06Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Bezrukavnikov, Roman
Ionov, Andrei
Massachusetts Institute of Technology. Department of Mathematics
2022-08-29T16:02:05Z
2022-08-29T16:02:05Z
2022-05
2022-08-16T16:39:38.177Z
https://hdl.handle.net/1721.1/144648
For a certain class of real analytic varieties with the real Lie group action we define a tstructure on the category of equivariant-monodromic sheaves and develop the theory of tilting sheaves. In case of a quasi-split real form of an algebraic group acting on the flag variety we construct an analog of a Soergel functor, which fully-faithfully embeds the subcategory of tilting objects to the category of coherent sheaves on a block variety. We apply the results to give a new, purely geometric, proof of the Soergel’s conjecture for quasi-split groups. The thesis is based on a joint work with Zhiwei Yun.
Ph.D.
Massachusetts Institute of Technology
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Tilting sheaves for real groups and Koszul duality
Thesis
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Doctoral
Doctor of Philosophy
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<Abstract>For a certain class of real analytic varieties with the real Lie group action we define a tstructure on the category of equivariant-monodromic sheaves and develop the theory of tilting sheaves. In case of a quasi-split real form of an algebraic group acting on the flag variety we construct an analog of a Soergel functor, which fully-faithfully embeds the subcategory of tilting objects to the category of coherent sheaves on a block variety. We apply the results to give a new, purely geometric, proof of the Soergel’s conjecture for quasi-split groups. The thesis is based on a joint work with Zhiwei Yun.</Abstract>
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