Abstract
With the help of operator-theoretic methods, we derive new and powerful criteria for finiteness of the uniton number for a harmonic map from a Riemann surface to the unitary group \({{\,\mathrm{U}\,}}(n)\). These use the Grassmannian model where harmonic maps are represented by families of shift-invariant subspaces of \(L^2(S^1,{{\mathbb {C}}}^n)\); we give a new description of that model.
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Communicated by Adrian Constantin.
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The second author was partially supported by Fundação para a Ciência e Tecnologia through the project UID/MAT/00212/2019.
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Aleman, A., Pacheco, R. & Wood, J.C. Harmonic maps and shift-invariant subspaces. Monatsh Math 194, 625–656 (2021). https://doi.org/10.1007/s00605-021-01516-w
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DOI: https://doi.org/10.1007/s00605-021-01516-w