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∨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.