A finiteness theorem of harmonic maps from compact lie groups toO HS(H)

In this article we study the behavior of harmonic maps from compact connected Lie groups with bi-invariant metrics into a Hilbert orthogonal group. In particular, we will demonstrate that any such harmonic map always has image contained within someO(n),n<∞. Since homomorphisms are a special subset of the harmonic maps we get as a corollary an extension of the Peter-Weyl theorem, namely, that every representation of a connected compact Lie group is finite dimensional. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.