This seminar aims to give an overview of results concerning special classes of integrable N-particle quantum systems. Specifically, we focus on elliptic Calogero-Moser systems of nonrelativistic (differential operator) and relativistic (difference operator) type, related to the Lie algebras $A_{N-1}$ and $BC_N$. In the last part we sketch our own approach to the construction of joint eigenfunctions, based on kernel functions that give rise to Hilbert-Schmidt integral operators.

University of Leeds, UK