  In this paper we study root system generalizations of the quantum Bose-gas on
the circle with pair-wise delta function interactions. The underlying symmetry
structures are shown to be governed by the associated graded of Cherednik's
(suitably filtered) degenerate double affine Hecke algebra, acting by
Dunkl-type differential-reflection operators. We use Gutkin's generalization of
the equivalence between the impenetrable Bose-gas and the free Fermi-gas to
derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.
