DIS

Abstract

This talk is concerned with elliptic Calogero-Moser quantum N-particle systems of nonrelativistic and relativistic type, associated with the Lie algebras A_{N-1} and BC_N. We outline various results from our ongoing programme to obtain suitable orthonormal joint eigenvector bases of the commuting Hamiltonians by employing special Hilbert-Schmidt operators. The integral kernels of the latter involve elliptic gamma functions in the relativistic (difference) case, and powers of theta functions in the nonrelativistic (differential) case.