Geodesic
Lie superalgebras and Calogero–Moser–Sutherland systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 136 (2017), pp. 72-102
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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, Lie superalgebra, symmetric function, Euler character, Grothendieck ring.
Mots-clés : Lax pair 
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     title = {Lie superalgebras and {Calogero{\textendash}Moser{\textendash}Sutherland} systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {72--102},
     year = {2017},
     volume = {136},
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A. N. Sergeev. Lie superalgebras and Calogero–Moser–Sutherland systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on algebra and geometry of the Samara University, Tome 136 (2017), pp. 72-102. http://geodesic.mathdoc.fr/item/INTO_2017_136_a3/