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 of eigenfunctions for the commuting quantum integrals in terms of Macdonald's three-parameter hyperoctahedral Hall-Littlewood polynomials. 
J.F. van Diejen, E. Emsiz and I.N. Zurri\'an
math-ph math.MP math.RT nlin.SI