All Harmonic 2-spheres in the Unitary Group, Completely Explicitly
نویسندگان
چکیده
We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual ∂-problems or loop group factorizations. We interpret our constructions using Segal’s Grassmannian model, giving an explicit factorization of the algebraic loop group, and showing how to obtain harmonic maps into a Grassmannian.
منابع مشابه
S ep 2 00 9 ALL HARMONIC 2 - SPHERES IN THE UNITARY GROUP , COMPLETELY EXPLICITLY
We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual ∂-problems or loop group factorizations. We interpret ...
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