Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions

Abstract

We provide explicit formulas for the quantum integrals of a semi-infinite $q$-boson system with boundary interactions. These operators and their commutativity are deduced from the Pieri formulas for a $q\to 0$ Hall-Littlewood type degeneration of the Macdonald-Koornwinder polynomials.

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