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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks
Mikhail Bershteinabcde, Roman Goninbd a Independent University of Moscow, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Landau Institute for Theoretical Physics, Chernogolovka, Russia
d Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia
e Institute for Information Transmission Problems, Moscow, Russia
Аннотация:
We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally identified with the basic level $1$ representation of affine $\mathfrak{gl}_n$. We also study twisted $W$-algebras of $\mathfrak{sl}_n$ 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.
Ключевые слова:
quantum algebras, toroidal algebras, $W$-algebras, conformal blocks, Nekrasov partition function, Whittaker vector.
Поступила: 22 ноября 2019 г.; в окончательном варианте 1 августа 2020 г.; опубликована 16 августа 2020 г.
Образец цитирования:
Mikhail Bershtein, Roman Gonin, “Twisted Representations of Algebra of $q$-Difference Operators, Twisted $q$-$W$ Algebras and Conformal Blocks”, SIGMA, 16 (2020), 077, 55 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1614 https://www.mathnet.ru/rus/sigma/v16/p77
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