## 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.

grunbaum@math.berkeley.edu