Vasily Krylov, MIT

Title: From geometric realizations of affine Hecke algebras to character formulas

Abstract: I will explain an approach allowing to extract character formulas for irreducible \hat{g}-modules at the positive level from the geometry of some open subvarieties of Steinberg varieties. The approach uses Bezrukavnikov’s “exotic coherent” categorification of the canonical basis of the affine Hecke algebra for g. We will discuss the first nontrivial example and will see that it leads to explicit character formulas for all irreducible modules (with integral highest weights) in categories O for certain Vertex algebras coming from the 4D/2D correspondence. Based on joint works with Bezrukavnikov, Kac, and Suzuki.