Drinfeld-Gaitsgory functor and Matsuki duality
Tsao-Hsien Chen
TL;DR
This paper establishes a formula relating the Drinfeld-Gaitsgory functor to Matsuki duality for K-equivariant sheaves on G's flag manifold, providing new insights into dualities in representation theory.
Contribution
It introduces a formula connecting the Drinfeld-Gaitsgory functor with Matsuki duality, advancing understanding of dualities in equivariant sheaves and (g,K)-modules.
Findings
Formula for Drinfeld-Gaitsgory functor in terms of Matsuki duality
Description of the Serre functor for (g,K)-modules
Description of Deligne-Lusztig duality for (g,K)-modules
Abstract
Let G be a connected complex reductive group and let K be a symmetric subgroup of G. We prove a formula for the Drinfeld-Gaitsgory functor for the dg-category of K-equivariant sheaves on the flag manifold of G in terms of the Matsuki duality functor. As byproducts, we obtain a description of the Serre functor and the Deligne-Lusztig duality for (g,K)-modules.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology