A k-symmetric shift-invariant subspace corresponds exactly to a filtration of invariant subspaces, yielding new general forms for extended solutions and a method to reverse the known construction of harmonic maps from primitive harmonic maps.
Harmonic maps and shift-invariant subspaces
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abstract
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of operator-theoretic methods we derive a criterion for finiteness of the uniton number which has a large number of applications discussed in the paper.
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2019 1verdicts
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Symmetric shift-invariant subspaces and harmonic maps
A k-symmetric shift-invariant subspace corresponds exactly to a filtration of invariant subspaces, yielding new general forms for extended solutions and a method to reverse the known construction of harmonic maps from primitive harmonic maps.