Twisted Fock module of toroidal algebra via DAHA and vertex operators
Abstract
We construct the twisted Fock module of quantum toroidal $\mathfrak{gl}_1$ algebra with a slope $n'/n$ using vertex operators of quantum affine $\mathfrak{gl}_n$. The proof is based on the $q$wedge construction of an integrable levelone $U_q(\widehat{\mathfrak{gl}}_n)$module and the representation theory of double affine Hecke algebra. The results are consistent with GorskyNeguţ conjecture (KononovSmirnov theorem) on stable envelopes for Hilbert schemes of points in the plane and can be viewed as a manifestation of $(\mathfrak{gl}_1,\mathfrak{gl}_n)$duality.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12598
 Bibcode:
 2021arXiv210912598B
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory