Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems

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.