The monodromy of real Bethe vectors for the Gaudin model

  • Noah White

    University of California, Los Angeles, USA
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Abstract

The Bethe algebras for the Gaudin model act on the multiplicity space of tensor products of irreducible glr\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 M0,n+1(R)\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 JnJ_n on tensor products of irreducible glr\mathfrak{gl}_r-crystals.

Cite this article

Noah White, The monodromy of real Bethe vectors for the Gaudin model. J. Comb. Algebra 2 (2018), no. 3, pp. 259–300

DOI 10.4171/JCA/2-3-3