Completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions
J.F. van Diejen, E. Emsiz, I.N. Zurri\'an
TL;DR
This paper proves the completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions, using advanced algebraic techniques and special functions.
Contribution
It introduces a novel algebraic framework employing the double affine Hecke algebra to establish the Bethe Ansatz completeness for the system.
Findings
Bethe Ansatz provides a complete eigenfunction basis.
Eigenfunctions are expressed via Macdonald's hyperoctahedral Hall-Littlewood polynomials.
The approach links algebraic structures with integrable quantum systems.
Abstract
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type at the critical level q=1, to endow the open finite -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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