The monodromy of real Bethe vectors for the Gaudin model
Autor: | Noah White |
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Rok vydání: | 2018 |
Předmět: |
Pure mathematics
Algebra and Number Theory Group (mathematics) Multiplicity (mathematics) Space (mathematics) Spectrum (topology) Bethe ansatz Tensor product Monodromy Simple (abstract algebra) Mathematics::Quantum Algebra FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
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 |
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