Séminaire de Mathématique

Monodromy of Bethe Ansatz Equation for the Gaudin Magnet Chain

par Leonid Rybnikov (HSE & IHES)

Europe/Paris
Centre de conférences Marilyn et James SImons (IHES)

Centre de conférences Marilyn et James SImons

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

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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