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Integrable boundary interactions for Ruijsenaars' difference Toda chain

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.

preprint2014arXivOpen access
J. F. van DiejenE. Emsiz
math-phmath.MPnlin.SI
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J. F. van DiejenE. Emsiz

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