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Hilbert-Schmidt operators vs. elliptic Calogero-Moser type systems

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Discrete Integrable Systems

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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