ON REALITY PROPERTY OF WRONSKI MAPS

Confluentes Mathematici

VARCHENKO, A¹  MUKHIN, E¹  TARASOV, V² 

[1] Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, 402 North Blackford St, Indianapolis, IN 46202-3216, USA;St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia

关键词: Discrete Wronski map;    B. and M. Shapiro conjecture;    Bethe ansatz;    XXX model;   

DOI  :  10.1142/S1793744209000092

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

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 theorem generalizes the statement of the B. and M. Shapiro conjecture about spaces of polynomials. The proof is based on the Bethe ansatz method for the XXX model.

【 授权许可】

Unknown