Tuesday, June 19, 2012

1206.3787 (Martin Hallnäs et al.)

Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of
hyperbolic type. I. First steps

Martin Hallnäs, Simon Ruijsenaars
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. The scheme is based on kernel identities we obtained in previous work. In this first paper of a series we present the formal features of the scheme, show explicitly its arbitrary-N viability for the `free' cases, and supply the analytic tools to prove the joint eigenfunction properties in suitable holomorphy domains.
View original: http://arxiv.org/abs/1206.3787

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