Projective loops generate rational loop groups
arXiv:1812.01456 · doi:10.1017/S1474748020000171
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).
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