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Annales Henri Poincaré

, Volume 19, Issue 5, pp 1349–1384 | Cite as

Completeness of the Bethe Ansatz for an Open \(\varvec{q}\)-Boson System with Integrable Boundary Interactions

  • Jan Felipe van Diejen
  • Erdal Emsiz
  • Ignacio Nahuel Zurrián
Article

Abstract

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level \(\text {q}=1\), 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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jan Felipe van Diejen
    • 1
  • Erdal Emsiz
    • 2
  • Ignacio Nahuel Zurrián
    • 2
  1. 1.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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