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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ISU_2017_17_1_a1,
     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/}
}
TY  - JOUR
AU  - G. S. Movsisyan
AU  - A. N. Sergeev
TI  - CMS operators type $ B (1,1)$ and Lie superalgebra $\mathfrak{osp}(3,2)$
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2017
SP  - 19
EP  - 30
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a1/
LA  - ru
ID  - ISU_2017_17_1_a1
ER  - 
%0 Journal Article
%A G. S. Movsisyan
%A A. N. Sergeev
%T CMS operators type $ B (1,1)$ and Lie superalgebra $\mathfrak{osp}(3,2)$
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2017
%P 19-30
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a1/
%G ru
%F ISU_2017_17_1_a1
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/

[1] Serganova V., “Characters of irreducible representations of simple Lie superalgebras”, Proc. Intern. Congress of Math. (Berlin, 1998), v. II, Doc. Math. Extra, 583–593 | MR | Zbl

[2] Sergeev A. N., Veselov A. P., “Deformed quantum Calogero–Moser systems and Lie superalgeras”, Commun. Math. Phys., 245:2 (2004), 249–248 | DOI | MR

[3] Sergeev A. N., Veselov A. P., “$BC_{\infty}$ Calogero–Moser operator and super Jacobi polynomials”, Advances in Mathematics, 222:5 (2009), 1687–1726 | DOI | MR | Zbl

[4] Sergeev A. N., Veselov A. P., “Generalised discriminant, deformed quantum Calogero–Moser–Sutherland problem and super-Jack polynomials”, Advances in Math., 192:2 (2005), 341–375 | DOI | MR | Zbl

[5] Gruson C., Serganova V., “Cohomology of generalized supergrassmanians and character formulae for basic classical Lie superalgebras”, Proc. London Math. Soc., 101:3 (2010), 852–892 | DOI | MR | Zbl