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

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Abstract

Using the approach developed by Gautam and Toledano Laredo, 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.

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Acknowledgments

The main result presented in this paper was mostly obtained during the author’s stay at IHES (Bures-sur-Ivette, France).

Funding

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).

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Oblast, Russia

    V. A. Stukopin

  2. Southern Mathematical Institute of the Vladikavkaz Scientific Center, RAS, Vladikavkaz, Russia

    V. A. Stukopin

  3. National Research University “Higher School of Economics”, Moscow, Russia

    V. A. Stukopin

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  1. V. A. Stukopin
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Correspondence to V. A. Stukopin.

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Stukopin, V.A. Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra. Theor Math Phys 204, 1227–1243 (2020). https://doi.org/10.1134/S0040577920090111

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  • DOI: https://doi.org/10.1134/S0040577920090111

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