HALLNÄS, M. and RUIJSENAARS, S., 2012. Kernel functions Bäcklund transformations for relativistic Calogero-Moser Toda systems. Journal of Mathematical Physics, 53 (12), http://dx.doi.org/10.1063/1.4764878, 64 pp.
We obtain kernel functions associated with the quantum relativistic Toda systems,
both for the periodic version and for the nonperiodic version with its dual. This
involves taking limits of previously known results concerning kernel functions for
the elliptic and hyperbolic relativistic Calogero-Moser systems. We show that the
special kernel functions at issue admit a limit that yields generating functions of
Bäcklund transformations for the classical relativistic Calogero-Moser and Toda
systems. We also obtain the nonrelativistic counterparts of our results, which tie
in with previous results in the literature.