Linear ODEs, Wronskians and Schubert Calculus
Algebraic Geometry
2013-10-15 v1 Classical Analysis and ODEs
Abstract
For a linear ODE with indeterminate coefficients, we explicitly exhibit a fundamental system of solutions, in terms of the coefficients. We show that the generalized Wronskians of the fundamental system are given by an action of the Schur functions on the usual Wronskian, and thence enjoy Pieri's and Giambelli's formulae. As an outcome, we obtain a natural isomorphism between the free module generated by the generalized Wronskians and the singular homology module of the Grassmannian.
Cite
@article{arxiv.1310.3345,
title = {Linear ODEs, Wronskians and Schubert Calculus},
author = {Letterio Gatto and Inna Scherbak},
journal= {arXiv preprint arXiv:1310.3345},
year = {2013}
}
Comments
17 Pages, appeared on Moscow Math. J., Volume 12, Number 2, April-June 2012, Pages 275-291