Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-11
Main Authors: van Diejen, J F, Emsiz, E, Zurrián, I N
Format: Article
Language:English
Subjects:
Eigenvectors
Integrals
Mathematical analysis
Polynomials
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level q=1, to endow the open finite \(q\)-boson system with integrable boundary interactions at the lattice ends. It is shown that the Bethe Ansatz entails a complete basis of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials.
ISSN:2331-8422
DOI:10.48550/arxiv.1611.05922