$A_{2}^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation

Details $A_{2}^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation $A_{2}^{(2)}$ Gaudin model and its associated Knizhnik-Zamolodchikov equation

2004-07-17

arxiv.org/abs/nlin/0407041v2

J.Phys. A38 (2005) 333-348

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages,no figure, typos corrected, LaTex

Scientific paper

10.1088/0305-4470/38/2/004

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.

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