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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84864110532
SN - 1609-3321
VL - 12
SP - 275
EP - 291
JO - Moscow Mathematical Journal
JF - Moscow Mathematical Journal
IS - 2
ER -