Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Bershtein, Mikhail, Gonin, Roman
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210771
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks. Mikhail Bershtein and Roman Gonin. SIGMA 16 (2020), 077, 55 pages

We study certain representations of the quantum toroidal ₁ algebra for = . We construct explicit bosonization of the Fock modules ⁽ⁿ′'ⁿ⁾ᵤ with a nontrivial slope ′/. As a vector space, it is naturally identified with the basic level 1 representation of affine ₙ. We also study twisted -algebras...