Commuting difference operators and the combinatorial Gale transform
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We develop the spectral theory of n-periodic strictly triangular difference operators L = T -k-1 + ∑ j=1 k a i j T−j and the spectral theory of the “superperiodic” operators for which all solutions of the equation (L + 1)ψ = 0 are (anti)periodic. We show that, for a superperiodic operator L of order k+1, there exists a unique superperiodic operator L of order n-k-1 which commutes with L and show that the duality L ↔ L coincides, up to a certain involution, with the combinatorial Gale transform recently introduced in .
Keywordsspectral theory of linear difference operators commuting difference operators frieze patterns moduli spaces of n-gons Gale transform
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