There is a bridge between generic linear Ordinary Differential Equations (ODEs), Schubert Calculus and the bosonic-fermionic representations of the Heisenberg algebra. For a finite-order generic linear ODE, the role of the bosonic space is played by the polynomial ring generated by the coefficients of the equation. The fermionic counterpart is constructed via wedging solutions to a generic linear ODE. Such natural spaces provide representations of Lie algebras which may be viewed as finitely generated approximations of the oscillator Heisenberg algebra. (C) 2014 Elsevier Inc. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)IBILCEUNESP, Campus of Sao Jose do Rio PretoPRIN "Geometria sulle Variet'a Algebriche"Politecnico di TorinoPolitecn Torino, Dipartimento Sci Matemat, Turin, ItalyIBILCE UNESP, Sao Jose Do Rio Preto, BrazilIBILCE UNESP, Sao Jose Do Rio Preto, BrazilFAPESP: 12/02869-1IBILCEUNESP, Campus of Sao Jose do Rio Preto0326/004/13-PROPG/CDCPRIN Geometria sulle Variet'a Algebriche2010S47ARA-009Politecnico di TorinoI. C. 11-RIL09CAS03