TY - JOUR

T1 - "On one property of one solution of one equation" or linear ODE's, wronskians and schubert calculus

AU - Gatto, L.

AU - Scherbak, I.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Fundamental solutions

KW - Generalized Wronskians

KW - Homology of the Grassmannian

KW - Linear ODEs

KW - Schur functions

UR - http://www.scopus.com/inward/record.url?scp=84864110532&partnerID=8YFLogxK

U2 - 10.17323/1609-4514-2012-12-2-275-291

DO - 10.17323/1609-4514-2012-12-2-275-291

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AN - SCOPUS:84864110532

SN - 1609-3321

VL - 12

SP - 275

EP - 291

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 2

ER -