Speaker: Valerio Toledano-Laredo (Northeastern University)

In person or on Zoom: https://mit.zoom.us/j/92441268505

Title: An abelian formula for the quantum Weyl group action of the coroot lattice

Abstract: I will describe an explicit formula for the quantum Weyl group action of the coroot lattice on finite-dimensional representations of a quantum loop algebra in terms of its commuting generators. The answer is expressed in terms of the Chari–Pressley series, whose evaluation on highest weight vectors gives rise to Drinfeld polynomials and hinges on a strong rationality result for that series. As an application, this identifies the action of the coroot lattice on the equivariant K–theory of Nakajima quiver varieties with that of explicitly given determinant line bundles.

This is joint work with Sachin Gautam based on arXiv:2501.02365