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

SIGMA 9 (2013), 077, 12 pages      arXiv:1312.1028      https://doi.org/10.3842/SIGMA.2013.077
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

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

Jan Felipe van Diejen and Erdal Emsiz
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

Received September 27, 2013, in final form November 26, 2013; Published online December 04, 2013

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.

Key words: Hall-Littlewood functions; q-bosons; boundary fields; hyperoctahedral symmetry.

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