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On reality property of Wronski maps

Research paper by E. Mukhin, V. Tarasov, A. Varchenko

Indexed on: 25 Mar '08Published on: 25 Mar '08Published in: Mathematics - Quantum Algebra



Abstract

We prove that if all roots of the discrete Wronskian with step 1 of a set of quasi-exponentials with real bases are real, simple and differ by at least 1, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result generalizes the B. and M.Shapiro conjecture about spaces of polynomials. The proof is based on the Bethe ansatz method for the XXX model.