Description
We construct the twisted Fock module of quantum toroidal gl_1 algebra with a slope n′/n using vertex operators of quantum affine gln. The proof is based on the q-wedge construction of an integrable level-one Uq(glˆn)-module and the representation theory of double affine Hecke algebra. The results are consistent with Gorsky-Neguţ conjecture (Kononov-Smirnov theorem) on stable envelopes for Hilbert schemes of points in the plane and can be viewed as a manifestation of (gl1,gln)-duality.
Based on joint work with R. Gonin
