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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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
Keywords and phrases
- quantum Calogero–Moser–Sutherland system
- Lax pair
- Lie superalgebra
- symmetric function
- Euler character
- Grothendieck ring