Symmetric shift-invariant subspaces and harmonic maps

Abstract

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and $k$-symmetric spaces. In particular, we obtain new general forms for such symmetric shift-invariant subspaces and for the corresponding extended solutions.

The original preprint `Harmonic maps and shift-invariant subspaces' was splitted in two. This is the second part. arXiv admin note: substantial text overlap with arXiv:1812.09379