Integrable boundary interactions for Ruijsenaars' difference Toda chain

Abstract

We endow Ruijsenaars' open difference Toda chain with a one-sided boundary interaction of Askey-Wilson type and diagonalize the quantum Hamiltonian by means of deformed hyperoctahedral $q$-Whittaker functions that arise as a $t=0$ degeneration of the Macdonald-Koornwinder multivariate Askey-Wilson polynomials. This immediately entails the quantum integrability, the bispectral dual system, and the $n$-particle scattering operator for the chain in question.

18 pages

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Cited by in corpus (4)

• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Branching Rules for Symmetric Hypergeometric Polynomials
• Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice
• Lax matrices for a 1-parameter subfamily of van Diejen--Toda chains