Trigonometric osp(1|2) Gaudin model

Details Trigonometric osp(1|2) Gaudin model Trigonometric osp(1|2) Gaudin model

2002-04-16

arxiv.org/abs/nlin/0204037v1

J.Math.Phys. 44 (2003) 676-700

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, LaTeX2e

Scientific paper

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.

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