Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Movsisyan G. S., Sergeev A. N. CMS Operators Type B(1, 1) and Lie Superalgebra osp(3, 2). Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 1, pp. 19-30. DOI: 10.18500/1816-9791-2017-17-1-19-30, EDN: YNBYAH

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CMS Operators Type B(1, 1) and Lie Superalgebra osp(3, 2)

Movsisyan Gevorg Surenovich, Saratov State University
Sergeev Alexander Nikolaevich, Saratov State University

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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