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Symmetric shift-invariant subspaces and harmonic maps

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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. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new results for the corresponding extended solutions, including how to obtain primitive harmonic maps from certain harmonic maps into the unitary group.

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Authors and Affiliations

  1. Mathematics, Faculty of Science, Lund University, P.O. Box 118, 22100, Lund, Sweden

    Alexandru Aleman

  2. Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, 6201-001, Covilhã, Portugal

    Rui Pacheco

  3. School of Mathematics, University of Leeds, G.B., Leeds, LS2 9JT, UK

    John C. Wood

Authors
  1. Alexandru Aleman
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  2. Rui Pacheco
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  3. John C. Wood
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Correspondence to Rui Pacheco.

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Rui Pacheco 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. Symmetric shift-invariant subspaces and harmonic maps. Math. Z. 299, 183–202 (2021). https://doi.org/10.1007/s00209-020-02680-9

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