Periodic integrable systems with delta-potentials

Details Periodic integrable systems with delta-potentials Periodic integrable systems with delta-potentials

2005-03-02

arxiv.org/abs/math/0503034v2

Commun.Math.Phys. 264 (2006) 191-225

Mathematics

Representation Theory

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

Scientific paper

10.1007/s00220-006-1519-6

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.

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