The Fock module is a basic representation of the quantum toroidal algebra; it can be identified with the equivariant K-theory of Hilbert schemes of points on C^2. We study a twisted Fock module, which is the same vector space, but the action is "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 (the conjecture of Gorsky and Negut on K-theoretic stable bases).

Zoom link: https://mit.zoom.us/j/96553931513