Cyclotomic Gaudin models, Miura opers and flag varieties
type: Item
instance of: scholarly article
title: Cyclotomic Gaudin models, Miura opers and flag varieties
zbMATH Open document ID: 1417.17032
author: S. Lacroix
author: B. Vicedo
published in: Annales Henri Poincaré
publication date: 2018-02-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1607.07397
full work available at URL: 1607.07397.pdf
review text: In this paper, the authors define cyclotomic \(\mathfrak{g}\)-opers over the Riemann sphere, given a semisimple Lie algebra \(\mathfrak{g}\). Moreover, the authors extend the notion of Miura \(\mathfrak{g}\)-opers to the cyclotomic setting. They prove that the subset of all cyclotomic Miura \(\mathfrak{g}\)-opers associated with the same cyclotomic \(\mathfrak{g}\)-oper is isomorphic to the \(\theta\)-invariant subset of the full flag variety of the adjoint groups \(G\) of \(\mathfrak{g}\), where the authomorphism \(\theta\) is specified in terms of certain data. The introduction of cyclotomic \(\mathfrak{g}\)-opers is motivated by the two conjectures relating them to the cyclotomic Gaudin model of the second author and \textit{C. Young} [Commun. Math. Phys. 343, No. 3, 971--1024 (2016; Zbl 1383.17016)].
reviewed by: Nenad Manojlović
Mathematics Subject Classification ID: 17B80
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 6837111
zbMATH Keywords: flag varieties
zbMATH Keywords: Miura opers
zbMATH Keywords: cyclotomic Gaudin algebras
MaRDI profile type: Publication
OpenAlex ID: W3099638589
arXiv ID: 1607.07397
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DOI: 10.1007/S00023-017-0616-8
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description: scientific article