Speaker: Shuai Wang (Columbia University)
Title:Monad realization of Hilb(T*P1), infinite dimensional Lie algebras and quantum multiplications
Abstract:In this talk we continue the study of the quantum cohomology on Hilb(T*P1), its equivariant limits and relations to representation theory of infinite dimensional Lie algebras. We first apply Lehn's formula to compute the classical multiplication of a certain divisor class on Hilb(T*P1). Then we use Frenkel-Kac construction to realize the purely quantum part as a vertex operator which lives in the basic representation of the affine sl_2. After utilizing Beilinson spectral sequence on Hirzebruch surfaces to give a monad description of Hilb(T*P1) as quiver varieties and match the tautological bundles, we demonstrate how to diagonalize the quantum multiplication operator and compute its eigenvalues via Bethe equations following Mina Aganagic, Andrei Okounkov, Nikita Nekrasov and Samson Shatashvili.