CMS operators type $ B (1,1)$ and Lie superalgebra $\mathfrak{osp}(3,2)$

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.