Séminaire "Equations différentielles"
Gaudin model is the simplest case of the quantum Hitchin system corresponding to the rational curve with marked points. Algebraic Bethe ansatz provides a general way to solve the eigenproblem of this quantum integrable system, it expresses the eigenvectors and the eigenvalues as some explicit functions on the auxiliary parameters which satisfy Bethe ansatz equations. The solutions of Bethe ansatz equations depend on the parameters of the integrable system, and this dependence is highly multivalued. We describe the monodromy of solutions of the Bethe ansatz equations and relate it to the RSK combinatorics of Young tableaux.
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Vasily Golyshev & Vladimir Roubtsov
