Spectrum of the Capelli basis of differential operators on superspaces

The algebra of invariant differential operators on a multiplicity-free representation of a reductive group has a concrete basis, usually referred to as the Capelli basis. The spectrum of the Capelli basis on spherical representations results in a family of symmetric polynomials (after \rho-shift) which has been studied extensively by Knop and Sahi in the early 1990's. In this talk, we generalize some of the Knop-Sahi results to the symmetric superpair GL(m,2n)/OSp(m,2n). We prove that in the Frobenius coordinates of Sergeev-Veselov, our polynomials turn into the shifted super Jack polynomials. This talk is based on joint work with Siddhartha Sahi.