Completeness of the Bethe Ansatz for an open q-boson system with integrable boundary interaction

ZURRIÁN IGNACIO

Baton Rouge

Seminario; Algebra Seminar; 2019

LSU

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type C∨C at the critical level 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 hyproctahedral Hall-Littlewood polynomials. This is a joint work with J.F. van Diejen and E. Emsiz.