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arXiv:math/0609428

On the new form of Bethe ansatz equations and separation of variables in the $sl_3$ Gaudin model

Evgeny Mukhin, Vadim V. Schechtman, V. Tarasov, Alexander N. Varchenko

Published Sep 15, 2006• 0 citations
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Abstract

A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum $sl_3$ Gaudin model is presented.

DOI
10.48550/arxiv.math/0609428

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On the new form of Bethe ansatz equations and separation of variables in the sl3sl_3sl3​ Gaudin model
A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum sl3sl_3sl3​ Gaudin model is presented.
On a new form of Bethe ansatz equations and separation of variables in the sl3\mathfrak{s}\mathfrak{l}_3 sl3​ Gaudin model
A new form of Bethe ansatz equations is introduced. A version of a separation of variables for the quantum sl3\mathfrak{s}\mathfrak{l}_3 sl3​ Gaudin model is presented.
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 ∣w1,w2)=∑n=0∞Pnn!∣w1,w2,0⟩, \left| {w_1 ,w_2 )} \right. = \sum\limits_{n = 0}^\infty {\frac{{P^n }} {{n!}}} \left| {w_1 ,w_2 ,0} \right\rangle , ∣w1​,w2​)=n=0∑∞​n!Pn​∣w1​,w2​,0⟩, where w 1, w 2 fulfil the standard well-know Bethe Ansatz equations.