  We prove that there is a natural grading-preserving isomorphism of
$\sl$-modules between the basic module of the affine Lie algebra $\widehat\sl$
(with the homogeneous grading) and a Schur--Weyl module of the infinite
symmetric group $\sinf$ with a grading defined through the combinatorial notion
of the major index of a Young tableau, and study the properties of this
isomorphism. The results reveal new and deep interrelations between the
representation theory of $\widehat\sl$ and the Virasoro algebra on the one
hand, and the representation theory of $\sinf$ and the related combinatorics on
the other hand.
