Twisted Representations of Algebra of qDifference Operators, Twisted qW Algebras and Conformal Blocks
Abstract
We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally identified with the basic level 1 representation of affine $\mathfrak{gl}_n$. We also study twisted $W$algebras of $\mathfrak{sl}_n$ acting on these Fock modules. As an application, we prove the relation on $q$deformed conformal blocks which was conjectured in the study of $q$deformation of isomonodromy/CFT correspondence.
 Publication:

SIGMA
 Pub Date:
 August 2020
 DOI:
 10.3842/SIGMA.2020.077
 arXiv:
 arXiv:1906.00600
 Bibcode:
 2020SIGMA..16..077B
 Keywords:

 quantum algebras; toroidal algebras; $W$algebras; conformal blocks; Nekrasov partition function; Whittaker vector;
 Mathematics  Representation Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 SIGMA 16 (2020), 077, 55 pages