Vasily Krylov (MIT) “From geometric realization of affine Hecke algebras to character formulas”

Seminar Organizer

Event Details

In the first part of the talk, I will recall Kazhdan-Lusztig’s geometric realization of the affine Hecke algebra H_q as well as Bezrukavnikov’s categorification of the statement. One of the fundamental tools of the theory is the so-called asymptotic affine Hecke algebra introduced by Lusztig (it can be thought of as a “limit” of H_q as “q goes to 0”). I will explain the geometric realization of this algebra (joint work with Bezrukavnikov and Karpov) and mention applications. In the second part, we will discuss one very concrete example of this story. Understanding of this example will lead us 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. The main “geometric” object of the second part of the talk will be very simple: the equivariant K-theory of the resolution of (arbitrary type) Kleinian singularity. The second part of the talk is based on joint works with Bezrukavnikov, Kac, and Suzuki.