The Monodromy of Real Bethe Vectors for the Gaudin Model
نویسنده
چکیده
The Bethe algebras for the Gaudin model act on the multiplicity space of tensor products of irreducible glr-modules and have simple spectrum over real points. This fact is proved by Mukhin, Tarasov and Varchenko who also develop a relationship to Schubert intersections over real points. We use an extension to M0,n+1(R) of these Schubert intersections, constructed by Speyer, to calculate the monodromy of the spectrum of the Bethe algebras. We show this monodromy is described by the action of the cactus group Jn on tensor products of irreducible glr-crystals.
منابع مشابه
ar X iv : c on d - m at / 9 90 83 26 v 1 2 4 A ug 1 99 9 Gaudin Hypothesis for the XY Z Spin Chain
The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.
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The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.
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The XY Z spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XY Z spin chain.
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