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Статья

Symmetric Lie superalgebras and deformed quantum Calogero–Moser problems

Advances in Mathematics. 2017. No. 304. P. 728-768.
Sergeev A., Veselov A.

The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero–Moser systems. In the special case of symmetric pair g=gl(n,2m),k=osp(n,2m)we establish a natural bijection between projective covers of spherically typical irreducible g-modules and the finite dimensional generalised eigenspaces of the algebra of Calogero–Moser integrals Dn,m acting on the corresponding Laurent quasi-invariants An,m.