English

On reality property of Wronski maps

Quantum Algebra 2008-03-25 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.0710.5856,
  title  = {On reality property of Wronski maps},
  author = {E. Mukhin and V. Tarasov and A. Varchenko},
  journal= {arXiv preprint arXiv:0710.5856},
  year   = {2008}
}

Comments

Latex, 20 pages