Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 037, 9 pages      arXiv:1505.01250      https://doi.org/10.3842/SIGMA.2015.037
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

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

Jan Felipe van Diejen a and 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

Received February 04, 2015, in final form April 30, 2015; Published online May 06, 2015

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.

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

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