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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 204, Number 3, Pages 466–484
DOI: https://doi.org/10.4213/tmf9894 (Mi tmf9894) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra

V. A. Stukopinabc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, , Moscow Oblast, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
c National Research University "Higher School of Economics", Moscow, Russia
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DOI: https://doi.org/10.4213/tmf9894
Abstract: Using the approach developed by Toledano Laredo and Gautam, we introduce analogues of the category $\mathfrak{O}$ for representations of the Yangian $Y_\hbar(A(m,n))$ of a special linear Lie superalgebra and the quantum loop superalgebra $U_q(LA(m,n))$. We investigate the relation between them and conjecture that these categories are equivalent.
Keywords: Yangian of Lie superalgebra, quantum loop superalgebra, Yangian module, category $\mathfrak{O}$ of representations, Lie superalgebra, Drinfeld polynomial, quantum $R$-matrix.
Funding agency Grant number
European Research Council QUASIFT 677368
This research was supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (QUASIFT Grant Agreement No. 677368).
Received: 29.02.2020
Revised: 28.04.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 204, Issue 3, Pages 1227–1243
DOI: https://doi.org/10.1134/S0040577920090111
Bibliographic databases:
Document Type: Article
MSC: 17B37, 81R50
Language: Russian
Citation: V. A. Stukopin, “Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra”, TMF, 204:3 (2020), 466–484; Theoret. and Math. Phys., 204:3 (2020), 1227–1243
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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