, Volume 47, Issue 2, pp 2473-2488

Separation of variables in the Gaudin model

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Abstract

We separate variables for the Gaudin model (degenerate case of an integrable quantum magnet SU(2) -chain) by means of an explicit change of coordinates. We get a description of the space of states in the language of ideals in polynomial rings. The structure of the eigenfunctions is studied.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 151–169, 1987.
The author thanks I. V. Komarov, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the work and helpful comments.