Special Analysis Seminar: Completeness of the Bethe Ansatz for an open \(q\)-boson system with integrable boundary interactions

Seminar | January 10 | 11 a.m.-12 p.m. | 939 Evans Hall

 Ignacio Zurrian, Universidad Nacional de Cordoba, Argentina

 Department of Mathematics

We employ a discrete integral-reflection representation of the double affine Hecke algebra of type \(C^\vee C\) 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.