  The integral singular cohomology ring of the Grassmann variety parametrizing
$r$-dimensional subspaces in the $n$-dimensional complex vector space is
naturally an irreducible representation of the Lie algebra of all the $n\times
n$ matrices with integral entries. Using the notion of Schubert derivation, a
distinguished Hasse-Schmidt derivation on an exterior algebra, we describe
explicitly such a representation, indicating its relationship with the
celebrated bosonic vertex representation of the Lie algebra of infinite
matrices due to Date, Jimbo, Kashiwara and Miwa.
