Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks
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...
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| Опубліковано в: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| ISSN: | 1815-0659 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210771 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks. Mikhail Bershtein and Roman Gonin. SIGMA 16 (2020), 077, 55 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862626994502500352 |
|---|---|
| author | Bershtein, Mikhail Gonin, Roman |
| author_facet | Bershtein, Mikhail Gonin, Roman |
| citation_txt | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks. Mikhail Bershtein and Roman Gonin. SIGMA 16 (2020), 077, 55 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 of sn acting on these Fock modules. As an application, we prove the relation on -deformed conformal blocks, which was conjectured in the study of -deformation of isomonodromy/CFT correspondence.
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| first_indexed | 2026-03-14T16:09:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210771 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T16:09:49Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bershtein, Mikhail Gonin, Roman 2025-12-17T14:32:12Z 2020 Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks. Mikhail Bershtein and Roman Gonin. SIGMA 16 (2020), 077, 55 pages 1815-0659 2020 Mathematics Subject Classification: 17B67; 17B69; 81R10 arXiv:1906.00600 https://nasplib.isofts.kiev.ua/handle/123456789/210771 https://doi.org/10.3842/SIGMA.2020.077 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 of sn acting on these Fock modules. As an application, we prove the relation on -deformed conformal blocks, which was conjectured in the study of -deformation of isomonodromy/CFT correspondence. We are grateful to B. Feigin, P. Gavrylenko, E. Gorsky, A. Negut, and J. Shiraishi for their interest in our work and discussions. The work is partially supported by the Russian Foundation of Basic Research under grant mol_a_ved 18-31-20062 and by the HSE University Basic Research Program jointly with the Russian Academic Excellence Project "5-100". R.G. was also supported in part by the Young Russian Mathematics Award. The results of Section 9 are obtained under the support of the Russian Science Foundation under grant19-11-00275. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks Article published earlier |
| spellingShingle | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks Bershtein, Mikhail Gonin, Roman |
| title | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks |
| title_full | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks |
| title_fullStr | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks |
| title_full_unstemmed | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks |
| title_short | Twisted Representations of Algebra of -Difference Operators, Twisted - Algebras and Conformal Blocks |
| title_sort | twisted representations of algebra of -difference operators, twisted - algebras and conformal blocks |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210771 |
| work_keys_str_mv | AT bershteinmikhail twistedrepresentationsofalgebraofdifferenceoperatorstwistedalgebrasandconformalblocks AT goninroman twistedrepresentationsofalgebraofdifferenceoperatorstwistedalgebrasandconformalblocks |