The monodromy of real Bethe vectors for the Gaudin model

Autor: Noah White
Rok vydání: 2018
Předmět:
Zdroj: Journal of Combinatorial Algebra. 2:259-300
ISSN: 2415-6302
DOI: 10.4171/jca/2-3-3
Popis: 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.
Comment: 35 pages
Databáze: OpenAIRE