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.
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