Twisted Representations of Algebra of π‘ž-Difference Operators, Twisted π‘ž-π‘Š Algebras and Conformal Blocks

We study certain representations of the quantum toroidal π–Œπ”©β‚ algebra for π‘ž = 𝘡. We construct explicit bosonization of the Fock modules 𝓕⁽ⁿ′'ⁿ⁾ᡀ with a nontrivial slope 𝑛′/𝑛. As a vector space, it is naturally identified with the basic level 1 representation of affine π–Œπ”©β‚™. We also study twisted...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2020
Main Authors: Bershtein, Mikhail, Gonin, Roman
Format: Article
Language:English
Published: Інститут ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΠΊΠΈ НАН Π£ΠΊΡ€Π°Ρ—Π½ΠΈ 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210771
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Twisted Representations of Algebra of π‘ž-Difference Operators, Twisted π‘ž-π‘Š Algebras and Conformal Blocks. Mikhail Bershtein and Roman Gonin. SIGMA 16 (2020), 077, 55 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We study certain representations of the quantum toroidal π–Œπ”©β‚ algebra for π‘ž = 𝘡. We construct explicit bosonization of the Fock modules 𝓕⁽ⁿ′'ⁿ⁾ᡀ with a nontrivial slope 𝑛′/𝑛. As a vector space, it is naturally identified with the basic level 1 representation of affine π–Œπ”©β‚™. We also study twisted π‘Š-algebras of s𝔩n acting on these Fock modules. As an application, we prove the relation on π‘ž-deformed conformal blocks, which was conjectured in the study of π‘ž-deformation of isomonodromy/CFT correspondence.
ISSN:1815-0659