The monodromy of real Bethe vectors for the Gaudin model

IF 0.6 2区 数学 Q3 MATHEMATICS
Noah White
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引用次数: 8

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 $-crystals.
Gaudin模型的实贝特向量的单属性
Gaudin模型的Bethe代数作用于不可约的$ \mathfrak{gl}_r $-模的张量积的多重空间,在实点上具有简单谱。Mukhin, Tarasov和Varchenko证明了这一事实,他们也在实点上发展了与舒伯特交集的关系。我们使用扩展到$ \overline{M}_{0,n+1}(\mathbb{R}) $的这些由Speyer构造的Schubert交点来计算Bethe代数谱的单性。我们用仙人掌群$ J_n $对不可约$ \mathfrak{gl}_r $-晶体张量积的作用来描述这一单态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
9
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