Geometric Representation Theory Seminar

Wednesday, May 13, 2020 at 3:00pm

Virtual Event

Featured SpeakerRoman Gonin (HSE/Skoltech/MIT)

Title :  Twisted Fock module of quantum toroidal gl_1


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).

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