"On one property of one solution of one equation" or linear ODE's, wronskians and schubert calculus

L. Gatto, I. Scherbak

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)275-291
Number of pages17
JournalMoscow Mathematical Journal
Volume12
Issue number2
DOIs
StatePublished - 2012

Keywords

  • Fundamental solutions
  • Generalized Wronskians
  • Homology of the Grassmannian
  • Linear ODEs
  • Schur functions

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