Shimura operators, interpolation polynomials, and integrable systems

We will give a brief account of how Shimura operators defined on Hermitian symmetric pairs are related to Okounkov interpolation polynomials of Type BC and then generalize this connection to the super case. In particular, we show that the Harish-Chandra isomorphism maps supersymmetric Shimura operators to the Sergeev–Veselov interpolation polynomials. We will also discuss some recent progress towards a better understanding of integrable systems related to the Calogero–Moser–Sutherland operators.