Arik Wilbert (University of Bonn), GMA Seminar

Title: From Kazhdan-Lusztig polynomials to Springer fibers of type D

Abstract: In the first part of this talk I will define parabolic Kazhdan-Lusztig polynomials of type D with respect to a maximal parabolic of type A and explain how to explicitly compute these recursively defined polynomials with the help of cup diagrams. Cup diagrams can be used to construct a so-called arc algebra of type D whose category of finite-dimensional modules is closely related to many interesting representation theoretic or geometric settings (e.g. infinite-dimensional representation theory of the orthogonal Lie algebra, perverse sheaves on isotropic Grassmannians, non-semisimple representation theory of Brauer algebras). The center of this arc algebra is isomorphic to the cohomology ring of a certain two-block Springer fiber of type D. The goal of the second part of this talk will be to explore the intricate topology of these singular varieties using parabolic Kazhdan-Lusztig polynomials and the cup diagram combinatorics.