A FINITENESS THEOREM OF HARMONIC MAPS FROM COMPACT LIE-GROUPS TO O-HS(H) - HARMONIC MAPS BETWEEN GROUPS

In this article we study the behavior of harmonic maps from compact co nnected Lie groups with hi-invariant metrics into a Hilbert orthogonal group. In particular, we will demonstrate that any such harmonic map always has image contained within some O(n),n < infinity. Since homomo rphisms are a special subset of the harmonic maps we get as a corollar y an extension of the Peter-Weyl theorem, namely, that every represent ation of a connected compact Lie group is finite dimensional.