Abstract:
We propose new formulas for eigenvectors of the Gaudin model in the $sl(3)$ case. The central point of the construction is the explicit form of some operator $P$, which is used for derivation of eigenvalues given by the formula
$$|w_1,w_2)=\sum \limits^{\infty}_{n=0} \frac{P^n}{n!} |w_1,w_2,0>,$$
where $w_1, w_2$ fulfil the standard well-know Bethe Ansatz equations.
Citation:
Č. Burdík, O. Navrátil, “New Formula for the Eigenvectors of the Gaudin Model in the $sl(3)$ Case”, Regul. Chaotic Dyn., 13:5 (2008), 403–416
\Bibitem{BurNav08}
\by {\v C}.~Burd{\'\i}k, O.~Navr{\' a}til
\paper New Formula for the Eigenvectors of the Gaudin Model in the $sl(3)$ Case
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 5
\pages 403--416
\mathnet{http://mi.mathnet.ru/rcd586}
\crossref{https://doi.org/10.1134/S156035470805002X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2448338}
\zmath{https://zbmath.org/?q=an:1229.81127}
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