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

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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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Authors and Affiliations

  1. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

    Jan Felipe van Diejen

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

    Erdal Emsiz & Ignacio Nahuel Zurrián

Authors
  1. Jan Felipe van Diejen
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  2. Erdal Emsiz
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  3. Ignacio Nahuel Zurrián
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Correspondence to Jan Felipe van Diejen.

Additional information

Communicated by Jean-Michel Maillet.

This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants # 1170179, # 1141114 and # 3160646.

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van Diejen, J.F., Emsiz, E. & Zurrián, I.N. Completeness of the Bethe Ansatz for an Open \(\varvec{q}\)-Boson System with Integrable Boundary Interactions. Ann. Henri Poincaré 19, 1349–1384 (2018). https://doi.org/10.1007/s00023-018-0658-6

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  • DOI: https://doi.org/10.1007/s00023-018-0658-6

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