Parameter space of harmonic maps of constant energy density into spheres (Q801343)

Given a compact (isotropy) irreducible Riemannian homogeneous space M and an eigenvalue \(\lambda\), equivalence classes of full harmonic maps \(f: M\to S^ n\) with energy density \(\lambda\) /2 can be parametrized by a compact convex body L lying in a finite dimensional vector space E. For \(M=S^ m\), the \(SO(m+1)\)-module structure of E is determined via the highest weight vectors of the irreducible components of E. Moreover, dim E\(=\dim L\) is computed for all m and \(\lambda\).