@article{6b992ceead914686a94a1355d33ef7d4,

title = "Twisted representations of algebra of q-difference operators, twisted q-W algebras and conformal blocks",

abstract = "We study certain representations of quantum toroidal gl1 algebra for q = t. We construct explicit bosonization of the Fock modules Fu(n′,n) with a nontrivial slope n′ /n. As a vector space, it is naturally identified with the basic level 1 representation of affine gln . We also study twisted W-algebras of sln 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.",

keywords = "Conformal blocks, Nekrasov partition function, Quantum algebras, Toroidal algebras, W-algebras, Whittaker vector",

author = "Mikhail Bershtein and Roman Gonin",

note = "Funding Information: We are grateful to B. Feigin, P. Gavrylenko, E. Gorsky, A. Negu¸t, J. Shiraishi, for interest to our work and discussions. The work is partially supported by Russian Foundation of Basic Research under grant mol a ved 18-31-20062 and by the HSE University Basic Research Program jointly with Russian Academic Excellence Project {\textquoteleft}5-100{\textquoteright}. R.G. was also supported in part by Young Russian Mathematics award. The results of Section 9 are obtained under the support of the Russian Science Foundation under grant 19-11-00275. Publisher Copyright: {\textcopyright} 2020, Institute of Mathematics. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

doi = "10.3842/SIGMA.2020.077",

language = "English",

volume = "16",

pages = "1--55",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

}