Harmonic maps between complex projective spaces

Using the DoCarmo-Wallach theory, we classify (homogeneous) polynomial harmonic maps of complex projective spaces into spheres and complex projective spaces in terms of finite dimensional moduli spaces. We make use of representation theory of the (special) unitary group to give, for a spherical range, the exact dimension and, for complex projective spaces, a lower bound of the dimension of the moduli spaces.Supported in part by NSF Grant DMS 8603172.Research done in part while the third named author was on leave at University of California, Berkeley.