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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 275–291 (Mi mmj467)  

This article is cited in 4 scientific papers (total in 4 papers)

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

L. Gattoa, I. Shcherbakb

a 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.

DOI: https://doi.org/10.17323/1609-4514-2012-12-2-275-291

Full text: http://www.ams.org/.../abst12-2-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14M15, 34A30, 55R40
Received: January 2, 2011
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Citation: L. Gatto, I. Shcherbak, “"On one Property of one Solution of one Equation" or Linear ODEs, Wronskians and Schubert Calculus”, Mosc. Math. J., 12:2 (2012), 275–291

Citation in format AMSBIB
\Bibitem{GatShc12}
\by L.~Gatto, I.~Shcherbak
\paper "On one Property of one Solution of one Equation" or Linear ODEs, Wronskians and Schubert Calculus
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 275--291
\mathnet{http://mi.mathnet.ru/mmj467}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-2-275-291}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978757}
\zmath{https://zbmath.org/?q=an:1257.14034}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309365900005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gatto L., Scherbak I., “On Generalized Wronskians”, Contribution to Algebraic Geometry: Impanga Lecture Note, EMS Ser. Congr. Rep., ed. Pragacz P., Eur. Math. Soc., 2012, 257–295  mathscinet  zmath  isi
    2. Gatto L., Salehyan P., “The Boson-Fermion Correspondence From Linear ODEs”, J. Algebra, 415 (2014), 162–183  crossref  mathscinet  zmath  isi  scopus
    3. Ch.-Ts. Chan, H. Irie, B. Niedner, Ch.-H. Yeh, “Wronskians, dualities and FZZT-Cardy branes”, Nucl. Phys. B, 910 (2016), 55–177  crossref  mathscinet  zmath  isi  scopus
    4. L. Gatto, D. Laksov, “From linear recurrence relations to linear ODEs with constant coefficients”, J. Algebra. Appl., 15:6 (2016), 1650109  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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