Periodic integrable systems with delta-potentials
arXiv:math/0503034 · doi:10.1007/s00220-006-1519-6
Abstract
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.
36 pages. The analysis of the propagation operator in Sections 5 and 6 is corrected and simplified. To appear in Comm. Math. Phys