Appears in collections : Representation theory, mathematical physics and integrable systems / Théorie des représentations, physique mathématique et systèmes intégrables, Distinguished women in mathematics, Exposés de recherche

We study invariant differential operators on representations of supergroups associated with simple Jordan superalgebras, in the classical case this problem goes back to Kostant. Eigenvalues of Capelli differential operators give interesting families of polynomials such as super Jack polynomials of Sergeev and Veselov and factorial Schur polynomials of Okounkov and Ivanov. We also discuss connection with deformed Calogero-Moser systems in the super case.