Projective loops generate rational loop groups
Differential Geometry
2023-06-22 v2 Group Theory
Exactly Solvable and Integrable Systems
Abstract
Rational loops played a central role in Uhlenbeck's construction of harmonic maps into U(n) (chiral model in physics), and they are generated by simple elements with one pole and one zero constructed from Hermitian projections. It has been believed for long time that nilpotent loops should be added to generate rational loop groups with noncompact reality conditions. We prove a somewhat unexpected theorem that projective loops are enough to generate the rational loop groups of GL(n,C), GL(n,R), and U(p, q).
Cite
@article{arxiv.1812.01456,
title = {Projective loops generate rational loop groups},
author = {Gang Wang and Oliver Goertsches and Erxiao Wang},
journal= {arXiv preprint arXiv:1812.01456},
year = {2023}
}
Comments
1. 'Text overlap' is due to the second author's old preprint on U(p,q) case with some gaps. 2. Sorry for the mistake on page 1, and we have revised it immediately. arXiv admin note: text overlap with arXiv:0910.1687