Periodic quantum integrable systems with delta function potential

(joint work in progress with E. Emsiz and J.Stokman, also see math.RT/0503034)

Abstract:

In this talk we discuss the quantum gas with delta function interaction and periodic boundary constraints and its generalization  to affine Weyl groups. The system ist governed by a graded version of Cherednik's degenerate double affine Hecke algebra. We discuss the Dunkl type operators and the Bethe-Ansatz equation. In the case of the Bose gas, we formulate some fundamental conjectures concerning the Bethe- Ansatz eigenfunctions of the system.