MIT Infinite Dimensional Algebra Seminar
Friday, October 07, 2022 at 3:00pm to 5:00pm
Building 2, 2-135
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Vasily Krylov (MIT Mathematics)
Title: Subregular nilpotent orbits and explicit character formulas for modules over affine Lie algebras.
Abstract: The talk is based on the joint work with Roman Bezrukavnikov and Victor Kac (arXiv:2209.08865). Let g be a simple Lie algebra and let $\hat{g}$ be the corresponding affine Lie algebra. It is known that characters of irreducible (highest weight) representations of $\hat{g}$ can be computed in terms of values at q=1 of affine (inverse) Kazhdan-Lusztig polynomials. These values can be computed recursively but there are no explicit formulas for them in general. The goal of this talk is to describe certain cases when we can compute the values above explicitly resulting in explicit formulas for characters of certain irreducible $\hat{g}$-modules (partly generalizing results of Kac and Wakimoto). The calculation relies on the description of the corresponding module over the affine Hecke algebra in terms of the equivariant $K$-theory of the Springer resolution. Time permitting we will discuss possible generalizations.
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