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.
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