Geodesic
CMS operators type $ B (1,1)$ and Lie superalgebra $\mathfrak{osp}(3,2)$
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 1, pp. 19-30

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The main purpose of this article is to study the realation between the representations theory of Lie superalgebras $\mathfrak{osp}(3,2)$ and the Calogero–Moser–Sutherland (CMS) $B(1,1)$ type differential operator. The differential operator depends polynomially on three parameters. The corresponding polynomial eigenfunctions also depend on three parameters; but in the general case, the coefficients of these eigenfunctions have a rational dependence on the parameters. The issue of specialization of eigenfunctions with given parameter values is an important and interesting question, especially in case of Lie superalgebras for which $k=p=-1.$ In this case, we prove that the character of irreducible finite-dimensional representations of Lie superalgebras $\mathfrak{osp}(3,2)$ can be obtained from the eigenfunctions of the CMS $B(1,1)$ type differential operator in case of the specializations mentioned above, considering that $k, p$ are also connected by some linear ratio. 
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     author = {G. S. Movsisyan and A. N. Sergeev},
     title = {CMS operators type $ B (1,1)$ and {Lie} superalgebra $\mathfrak{osp}(3,2)$},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {19--30},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a1/}
}
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G. S. Movsisyan; A. N. Sergeev. CMS operators type $ B (1,1)$ and Lie superalgebra $\mathfrak{osp}(3,2)$. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 1, pp. 19-30. http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a1/