This article is cited in 10 papers

"On one Property of one Solution of one Equation" or Linear ODEs, Wronskians and Schubert Calculus

L. Gatto^a, I. Shcherbak<sup>b

a</sup> Dipartimento di Matematica, Politecnico di Torino, ITALY
^b School of Mathematical Sciences, Tel Aviv University, ISRAEL

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.

Key words and phrases: linear ODEs, fundamental solutions, generalized Wronskians, Schur functions, homology of the Grassmannian.

MSC: 14M15, 34A30, 55R40

Received: January 2, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-2-275-291

Bibliographic databases:

• 
• 
•