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arXiv · 1511.04740

The monodromy of real Bethe vectors for the Gaudin model

Noah White
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Abstract

The Bethe algebras for the Gaudin model act on the multiplicity space of tensor products of irreducible $ \mathfrak{gl}_r $-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 $ \overline{M}_{0,n+1}(\mathbb{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 $ J_n $ on tensor products of irreducible $ \mathfrak{gl}_r $-crystals.

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Noah White. 2015-11-15. The monodromy of real Bethe vectors for the Gaudin model. https://arxiv.org/abs/1511.04740

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