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

Abstract

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.

arXiv comment31 pages, LaTeX

References in corpus (12)

• Correlation functions for a strongly correlated boson system
• On integrability of zero-range chipping models with factorized steady state
• The sl(n)-WZNW Fusion Ring: a combinatorial construction and a realisation as quotient of quantum cohomology
• Spectral theory for the q-Boson particle system
• Boxed Plane Partitions as an Exactly Solvable Boson Model
• Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• Periodic integrable systems with delta-potentials
• Loop groups, anyons and the Calogero-Sutherland model
• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• A deformation of affine Hecke algebra and integrable stochastic particle system
• Second quantization of the elliptic Calogero-Sutherland model

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• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Discrete Fourier transform associated with generalized Schur polynomials
• Boson Sampling for Generalized Bosons
• Solutions of convex Bethe Ansatz equations and the zeros of (basic) hypergeometric orthogonal polynomials
• Cubature rules from Hall-Littlewood polynomials
• Spectral analysis of an open $q$-difference Toda chain with two-sided boundary interactions on the finite integer lattice
• On the basic representation of the double affine Hecke algebra at critical level