June 29: Roman Gonin (Moscow, HSE&Skoltech)

Title: Twisted representations of toroidal gl_1

Abstract:

Fock module is a basic representation of quantum toroidal gl1; it can be identified with equivariant K-theory of Hilbert scheme of points on C^2. We study a twisted Fock module which is the same vector space with an action "twisted by a certain automorphism of the algebra". Surprisingly, an attempt "to make this action explicit" leads to an appearance of an auxiliary quantum affine gl_n-action on (twisted) Fock space. I will explain our purely algebraic construction and formulate a conjectural application to geometry (conjecture of Gorsky and Negut on K-theoretic stable bases).