Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems

Abstract

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.

76 pages

References in corpus (3)

• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))
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