Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 136, Pages 72–102 (Mi into200)  
Lie superalgebras and Calogero–Moser–Sutherland systems

A. N. Sergeevab

a National Research University "Higher School of Economics" (HSE), Moscow
b Saratov State University
Full-text PDF (389 kB)
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.
Keywords: quantum Calogero–Moser–Sutherland system, Lax pair, Lie superalgebra, symmetric function, Euler character, Grothendieck ring.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Тhis work was partially supported by the Russian Academic Excellence Project “5–100.”
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 235, Issue 6, Pages 756–787
DOI: https://doi.org/10.1007/s10958-018-4092-6
Bibliographic databases:
Document Type: Article
UDC: 512.554.3, 514.84
MSC: 17B10, 17B22, 81U15
Language: Russian
Citation: A. N. Sergeev, “Lie superalgebras and Calogero–Moser–Sutherland systems”, Proceedings of the Seminar on algebra and geometry of the Samara University, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 136, VINITI, Moscow, 2017, 72–102; J. Math. Sci. (N. Y.), 235:6 (2018), 756–787
Citation in format AMSBIB
\Bibitem{Ser17}
\by A.~N.~Sergeev
\paper Lie superalgebras and Calogero--Moser--Sutherland systems
\inbook Proceedings of the Seminar on algebra and geometry of the Samara University
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 136
\pages 72--102
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3808188}
\zmath{https://zbmath.org/?q=an:07001314}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 235
\issue 6
\pages 756--787
\crossref{https://doi.org/10.1007/s10958-018-4092-6}
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