The semi-infinite q-boson system with boundary interaction

Understand

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction.

• The eigenfunctions are shown to be given by Macdonald's hyperoctahedral Hall-Littlewood functions of type BC.
• It follows that the n-particle spectrum is bounded and absolutely continuous and that the corresponding scattering matrix factorizes as a product of two-particle bulk and one-particle boundary scattering matrices.