Boundary interactions for the semi-infinite \(q\)-boson system and hyperoctahedral Hall-Littlewood polynomials. (English) Zbl 1292.81078
Summary: We present a semi-infinite \(q\)-boson system endowed with a four-parameter boundary interaction. The \(n\)-particle Hamiltonian is diagonalized by generalized Hall-Littlewood polynomials with hyperoctahedral symmetry that arise as a degeneration of the Macdonald-Koornwinder polynomials and were recently studied in detail by Venkateswaran.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 33D52 | Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) |
| 81T25 | Quantum field theory on lattices |
| 82B23 | Exactly solvable models; Bethe ansatz |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81V70 | Many-body theory; quantum Hall effect |
