Completeness of the Bethe ansatz for an open \(q\)-Boson system with integrable boundary interactions. (English) Zbl 1388.81240
Summary: We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) at the critical level \(\mathrm{q}=1\), 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.
MSC:
| 81S22 | Open systems, reduced dynamics, master equations, decoherence |
| 81T25 | Quantum field theory on lattices |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 81V70 | Many-body theory; quantum Hall effect |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
| 42B25 | Maximal functions, Littlewood-Paley theory |
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