\(\mathcal R\)-matrix and Baxter \(\mathcal Q\)-operators for the noncompact \(\mathrm{SL}(N,\mathbb C)\) invariant spin chain
type: Item
instance of: scholarly article
title: \(\mathcal R\)-matrix and Baxter \(\mathcal Q\)-operators for the noncompact \(\mathrm{SL}(N,\mathbb C)\) invariant spin chain
zbMATH Open document ID: 1138.82009
DOI: 10.3842/SIGMA.2006.084
published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
publication date: 2008-02-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/nlin/0612003
full work available at URL: https://eudml.org/doc/54159
full work available at URL: Paper084
review text: In this article, one constructs the \(\text{SL}(N,\mathbb C)\) invariant \(R\)-operator which acts on the tensor product of two principal series representations of the \(\text{SL}(N,\mathbb C)\) group. The \(R\)-operator is obtained in the form of the product of elementary operators \(U_{k}, k=1,\dots,2N-1\), which satisfy commutation relations similar to those of the operators of the standard permutation. This result has direct application to the Baxter operators, and provides a simple proof of the Yang-Baxter relation.
Mathematics Subject Classification ID: 82B23
Mathematics Subject Classification ID: 82B20
zbMATH DE Number: 5236993
zbMATH Keywords: Yang-Baxter equation
zbMATH Keywords: Baxter perator
author: S. É. Derkachov
author: Alexander N. Manashov
reviewed by: Guy Jumarie
MaRDI profile type: Publication
arXiv ID: nlin/0612003
OpenAlex ID: W2130094471
description: scientific article