The boson–fermion correspondence from linear ODEs

Abstract

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.