Tilting sheaves for real groups and Koszul duality
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ionov-aionov-phd-mathematics-2022-thesis.pdf
Description
Thesis PDF
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895.02 KB
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Author(s)
Ionov, Andrei
Advisor(s)
Bezrukavnikov, Roman
Date Issued
May 2022
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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