Boundary Interactions for the Semi-Infinite $q$-Boson System and Hyperoctahedral Hall–Littlewood Polynomials

We present a semi-infinite $q$-boson system endowed with a four-parameter boundary interaction. The $n$-particle Hamiltonian is diagonalized by generalized Hall–Littlewood polynomials with hyperoctahedral symmetry that arise as a degeneration of the Macdonald–Koornwinder polynomials and were recently studied in detail by Venkateswaran.