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Lie Superalgebras and Calogero–Moser–Sutherland Systems

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Abstract

We review recent results obtained at the intersection of the theory of quantum deformed Calogero–Moser–Sutherland systems and the theory of Lie superalgebras. We begin with a definition of admissible deformations of root systems of basic classical Lie superalgebras. For classical series, we prove the existence of Lax pairs. Connections between infinite-dimensional Calogero–Moser–Sutherland systems, deformed quantum CMS systems, and representation theory of Lie superalgebras are discussed.

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Authors and Affiliations

  1. N. G. Chernyshevsky Saratov State University, Saratov, Russia

    A. N. Sergeev

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

    A. N. Sergeev

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  1. A. N. Sergeev
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Correspondence to A. N. Sergeev.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 136, Proceedings of the Seminar on Algebra and Geometry of Samara University, 2017.

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Sergeev, A.N. Lie Superalgebras and Calogero–Moser–Sutherland Systems. J Math Sci 235, 756–787 (2018). https://doi.org/10.1007/s10958-018-4092-6

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  • DOI: https://doi.org/10.1007/s10958-018-4092-6

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