On reality property of Wronski maps

2007/10/31 by E. Mukhin, Mukhin, E., V. Tarasov +4
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.0710.5856

Latex, 20 pages

openalex publication_date 2007/10/31 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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