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Periodic integrable systems with delta-potentials

Representation Theory 2009-06-04 v2 High Energy Physics - Theory Mathematical Physics math.MP

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.

Cite

@article{arxiv.math/0503034,
  title  = {Periodic integrable systems with delta-potentials},
  author = {Erdal Emsiz and Eric M. Opdam and Jasper V. Stokman},
  journal= {arXiv preprint arXiv:math/0503034},
  year   = {2009}
}

Comments

36 pages. The analysis of the propagation operator in Sections 5 and 6 is corrected and simplified. To appear in Comm. Math. Phys