Extended solutions of the harmonic map equation in the special unitary group
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.53063
published in: The Quarterly Journal of Mathematics
publication date: 2014-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.4264
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 22E67
zbMATH DE Number: 6353654
zbMATH Keywords: Riemann surface
zbMATH Keywords: harmonic map
zbMATH Keywords: unitary group
zbMATH Keywords: loop space
zbMATH Keywords: uniton number
author: Nuno Correia
author: Rui Pacheco
MaRDI profile type: Publication
OpenAlex ID: W2030541450
arXiv ID: 1304.4264
DOI: 10.1093/QMATH/HAT018
title: Extended solutions of the harmonic map equation in the special unitary group
review text: Harmonic maps from a Riemann surface \(M\) into a Lie group \(G\) correspond by integration to certain holomorphic maps (the extended solutions) into the group \(\Omega G\) of based smooth loops in \(G\). If the Fourier series associated to an extended solution has finitely many terms, it is said that this solution and the corresponding harmonic map have ``finite uniton number''. For example, all harmonic maps from the two-sphere \(M=S^2\) have finite uniton number.NEWLINENEWLINEIn this paper all harmonic maps with finite uniton number from \(M\) into the special unitary group \(\mathrm {SU} (n)\) and the corresponding inner symmetric spaces (complex Grassmannians) are classified in terms of certain pieces of the Bruhat decomposition of \(\Omega_{\mathrm{alg}} \mathrm{SU} (n)\) (algebraic loop space).
reviewed by: V. V. Gorbatsevich
description: scientific article; zbMATH DE number 6353654