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

Mikhail Bershtein, Roman Gonin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Article number077
Pages (from-to)1-55
Number of pages55
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume16
DOIs
Publication statusPublished - 2020

Keywords

  • Conformal blocks
  • Nekrasov partition function
  • Quantum algebras
  • Toroidal algebras
  • W-algebras
  • Whittaker vector

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