Abstract
We present an explicit description of all harmonic maps of finite uniton number from a Riemann surface into a complex Grassmannian. Namely, starting from a constant map Q and a collection of meromorphic functions and their derivatives, we show how to algebraically construct all harmonic maps from the two-sphere into a given Grassmannian \({G_p(\mathbb C^n)}\) . In this setting the uniton number depends on Q and p and we obtain a sharp estimate for it.
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