Trigonometric osp(1|2) Gaudin model

Abstract

The problems connected with Gaudin models are reviewed by analyzing model related to the trigonometric osp(1|2) classical r-matrix. The eigenvectors of the trigonometric osp(1|2) Gaudin Hamiltonians are found using explicitly constructed creation operators. The commutation relations between the creation operators and the generators of the trigonometric loop superalgebra are calculated. The coordinate representation of the Bethe states is presented. The relation between the Bethe vectors and solutions to the Knizhnik-Zamolodchikov equation yields the norm of the eigenvectors. The generalized Knizhnik-Zamolodchikov system is discussed both in the rational and in the trigonometric case.

27 pages, LaTeX2e

References in corpus (4)

• Integrable model for interacting electrons in metallic grains
• Creation operators and Bethe vectors of the osp(1|2) Gaudin model
• Supersymmetric t-J Gaudin Models and KZ Equations
• The extension to the transverse momentum of the statistical parton distributions

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• $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms
• The $q$-boson-fermion realizations of quantum suprealgebra $U_q(gl(2/1))$
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish