Harmonic maps and shift-invariant subspaces

@article{Aleman2018HarmonicMA,
  title={Harmonic maps and shift-invariant subspaces},
  author={Alexandru Aleman and Rui Pacheco and John C. Wood},
  journal={arXiv: Functional Analysis},
  year={2018}
}
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models which 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. In the second part of the paper we impose a natural symmetry condition on the shift-invariant subspaces that… 
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