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

Abstract

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.

Keywords

• Hall-Littlewood functions
• q-bosons
• boundary fields
• hyperoctahedral symmetry