\(Sp(n)\)-equivariant harmonic maps between complex projective spaces
The author studies the existence and harmonicity of \(Sp(n)\)-equivariant maps between complex projective spaces by using the fact that the symplectic group \(Sp(n)\) acts on a \((2n-1)\)-dimensional complex projective space \(\mathbb{C} P^{2n-1}\) transitively. All complex irreducible representations of \(Sp(n)\) which define \(Sp(n)\)-equivariant maps from \(\mathbb{C} P^{2n-1}\) to \(\mathbb{C} P^m\) are determined. The author proves that the associated \(Sp(n)\)-equivariant maps are harmonic for any \(Sp(n)\)-invariant Riemannian metric on \(\mathbb{C} P^{2n-1}\). He obtains \(Sp(n)\)-equivariant minimal immersions from \(\mathbb{C} P^{2n-1}\) to \(\mathbb{C} P^m\), but not \(SU(2n)\)-equivariant ones.
scientific article; zbMATH DE number 1102803