Bispectral dual difference equations for the quantum Toda chain with boundary perturbations

Abstract

We show that hyperoctahedral Whittaker functions---diagonalizing an open quantum Toda chain with one-sided boundary potentials of Morse type---satisfy a dual system of difference equations in the spectral variable. This extends a well-known bispectral duality between the nonperturbed open quantum Toda chain and a strong-coupling limit of the rational Macdonald-Ruijsenaars difference operators. It is manifest from the difference equations in question that the hyperoctahedral Whittaker function is entire as a function of the spectral variable.

20 pages, LaTeX. To appear in Int. Math. Res. Not. IMRN

References in corpus (2)

• Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
• Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction

Cited by in corpus (1)

• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions