Cite this article as:
Movsisyan G. S., Sergeev A. N. CMS Operators Type B(1, 1) and Lie Superalgebra osp(3, 2). Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2017, vol. 17, iss. 1, pp. 19-30. DOI: https://doi.org/10.18500/1816-9791-2017-17-1-19-30
CMS Operators Type B(1, 1) and Lie Superalgebra osp(3, 2)
The main purpose of this article is to study the realation between the representations theory of Lie superalgebras 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 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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