Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems
arXiv:1412.8768
Abstract
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 D_{n,m} acting on the corresponding Laurent quasi-invariants A_{n,m}.
Extended version with minor corrections. A section with an explicit analysis of the simplest case m=n=1 is added