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VOL. 62 | 2012 Three sides of the geometric Langlands correspondence for $\mathfrak{gl}_N$ Gaudin model and Bethe vector averaging maps
Eugene Mukhin, Vitaly Tarasov, Alexander Varchenko

Editor(s) Hiroaki Terao, Sergey Yuzvinsky


We consider the $\mathfrak{gl}_N$ Gaudin model of a tensor power of the standard vector representation. The geometric Langlands correspondence in the Gaudin model relates the Bethe algebra of the commuting Gaudin Hamiltonians and the algebra of functions on a suitable space of $N$-th order differential operators. In this paper we introduce a third side of the correspondence: the algebra of functions on the critical set of a master function. We construct isomorphisms of the third algebra and the first two. Our main technical tool is the Bethe vector averaging maps, which is a new object.


Published: 1 January 2012
First available in Project Euclid: 24 November 2018

zbMATH: 1260.82025
MathSciNet: MR2933807

Digital Object Identifier: 10.2969/aspm/06210475

Primary: 82B23
Secondary: 17B80 , 32S22

Keywords: Bethe algebra , Bethe anzats , Bethe vector averaging map , critical points , master function , Wronsky map

Rights: Copyright © 2012 Mathematical Society of Japan


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