Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.82021
author: A. Varchenko
author: E. Mukhin
author: Vitaly O. Tarasov
publication date: 2014-09-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/0906.5185
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81R12
zbMATH DE Number: 6340347
zbMATH Keywords: Bethe algebra
zbMATH Keywords: Gaudin model
zbMATH Keywords: Galoger-Mozer space
zbMATH Keywords: Cherednik algebra
MaRDI profile type: Publication
OpenAlex ID: W2063045682
arXiv ID: 0906.5185
DOI: 10.1093/IMRN/RNS245
published in: IMRN. International Mathematics Research Notices
title: Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra
review text: The Bethe algebra of the Gaudin model associated to the complex Lie algebra \(\mathfrak{gl}_N\) of all \(N\times N\) matrices is a commutative subalgebra of the universal enveloping algebra of the current algebra of \(\mathfrak{gl}_N\). The Bethe algebra acts on a subspace \(M\) of any \(\mathfrak{gl}_N[t]\)-module consisting of all vectors of a fixed \(\mathfrak{gl}_N\)weight, producing a commutative family of linear operators \(\mathcal{B}(M)\in \mathrm{End} M\). The authors proved that \(\mathcal{B}(M)\) is naturally isomorphic to the center of the rational Cherednik algebra at the critical level of type \(A\) and that \(\mathcal{B}(M)\) is naturally isomorphic to the algebra \(\mathcal{O}_\chi\) of regular functions on the Calogero-Mozer space.
reviewed by: Nasir N. Ganikhodjaev
description: scientific article; zbMATH DE number 6340347