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.

中文翻译：

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对称移位不变子空间和调和图

Grassmannian模型通过Hilbert空间的位移不变子空间族表示Riemann曲面的谐波映射。我们在不变位移子空间上施加自然对称条件，这对应于将一类重要的谐波映射考虑为对称和k对称空间。使用这种对称的位移不变子空间的适当描述，我们为相应的扩展解获得了新的结​​果，包括如何从某些谐波图获得单一谐波图获得原始谐波图。