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

Ruijsenaars, S (Leeds/Loughborough)
Monday 29 June 2009, 10:00-11:00

Seminar Room 1, Newton Institute


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.


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