Harmonic maps and shift-invariant subspaces
arXiv:1812.09379
Abstract
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of operator-theoretic methods we derive a criterion for finiteness of the uniton number which has a large number of applications discussed in the paper.
Treatment of Grassmannian model clarified and relation with work of M. Guest added