{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/144648"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/144648","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Tilting sheaves for real groups and Koszul duality","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_html":"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_has_math":false,"creators":["Ionov, Andrei"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Tilting sheaves for real groups and Koszul duality"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bezrukavnikov, Roman"],"dc:contributor.department":["Massachusetts Institute of Technology. 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