Jan Felipe van Diejen, Erdal Emsiz, “Quantum Integrals for a Semi-Infinite <nobr>$q$</nobr>-Boson System with Boundary Interactions”, SIGMA, 2015, Volume 11,037, 9 pp.

This article is cited in 3 papers

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

Jan Felipe van Diejen^a, Erdal Emsiz^b

^a Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
^b Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

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.

Keywords: $q$-bosons; boundary interactions; Hall–Littlewood functions; hyperoctahedral symmetry; Pieri formulas; integrability.

MSC: 33D52; 81R50; 81T25; 82B23

Received: February 4, 2015; in final form April 30, 2015; Published online May 6, 2015

Language: English

DOI: 10.3842/SIGMA.2015.037