2009/09/30 by Martin Svensson, Svensson, Martin, John C. Wood +1
Mathematics · #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C43 #msc:58E20
paper · pdf · doi:10.48550/arxiv.0909.5582
Some minor improvements and corrections made
arxiv created 2010/08/11 · arxiv updated 2010/08/12
We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formulae for such harmonic maps to each of the classical compact Lie groups and their inner symmetric spaces - the nonlinear sigma-model of particle physics. Our methods also give an explicit Iwasawa decomposition of the algebraic loop group.