2025/01/04 by Gautam, S., Toledano-Laredo, V.
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2501.02365
Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coroot lattice Q of g on finite-dimensional representations of Uq(Lg) 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. It hinges on a strong rationality result for that series, which is derived in the present paper. As an application, we identify the action of Q on the equivariant K-theory of Nakajima quiver varieties with that of explicitly given determinant line bundles.