A useful technique in representation theory is localization. This relates categories of Lie algebra representations and categories of sheaves, and allows one to solve representation theoretic problems using geometry. We will begin by surveying for nonspecialists the works of Beilinson--Bernstein, Bezrukavnikov--Mirkovic--Rumynin, Kashiwara--Tanisaki, and Backelin--Kremnizer, which relate representations of semisimple and affine Lie algebras to D-modules on partial flag varieties. We will then describe some recent work, joint with Justin Campbell, which provides an alternative localization as D-modules on Whittaker flag manifolds, and time permitting discuss some applications.
Zoom link: https://unsw.zoom.us/j/83492167515?pwd=ZU5HNENGY0g0N0IrL3Y1emlBNmZ5Zz09
Thu, 03/03/2022 - 12:00pm
Online (see abstract for Zoom link)