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.

中文翻译：

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调和图和不变位移子空间

借助算子理论方法，我们为从Riemann曲面到the群\（{{\，\ mathrm {U} \，}}（n ）\）。这些使用格拉斯曼模型，其中谐波映射由\（L ^ 2（S ^ 1，{{\ mathbb {C}}} ^ n）\）的不变位移子空间族表示。我们对该模型进行了新的描述。