CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Obtaining Koszul Gradings Sarah Kitchen, Universitaet Freiburg
September 25, 2012 Math 350 2-3pm	Abstract This is a report on work in progress with Achar, McGerty, and Nevins. Koszul duality is a type of derived equivalence that appears in representation theory. It is expected to relate various categories of representations for Langlands dual pairs of Lie algebras, and underlie observed examples of duality in symplectic geometry. For a given abelian category, the derived equivalence does not occur at the level of the derived category of our abelian category, but for some graded version of the category. Obtaining a graded version and verifying that we have given one suitable for Koszul duality are not usually easy processes. In earlier work with Achar, we produced a grading on perverse sheaves with a fixed stratification from a candidate subcategory of mixed Hodge modules. In this talk, I will describe a more general context in which we can check if a mixed category is a grading suitable for Koszul duality.

Obtaining Koszul Gradings

Sarah Kitchen, Universitaet Freiburg

September 25, 2012

Math 350

2-3pm

Abstract

This is a report on work in progress with Achar, McGerty, and Nevins. Koszul duality is a type of derived equivalence that appears in representation theory. It is expected to relate various categories of representations for Langlands dual pairs of Lie algebras, and underlie observed examples of duality in symplectic geometry. For a given abelian category, the derived equivalence does not occur at the level of the derived category of our abelian category, but for some graded version of the category. Obtaining a graded version and verifying that we have given one suitable for Koszul duality are not usually easy processes. In earlier work with Achar, we produced a grading on perverse sheaves with a fixed stratification from a candidate subcategory of mixed Hodge modules. In this talk, I will describe a more general context in which we can check if a mixed category is a grading suitable for Koszul duality.