Periodic Integrable Systems with Delta-Potentials |
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Authors: | E Emsiz EM Opdam JV Stokman |
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Institution: | (1) KdV Institute for Mathematics, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands |
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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 algebra 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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