  Using a finite-dimensional Clifford algebra a new combinatorial product
formula for the small quantum cohomology ring of the complex Grassmannian is
presented. In particular, Gromov-Witten invariants can be expressed through
certain elements in the Clifford algebra, this leads to a q-deformation of the
Racah-Speiser algorithm allowing for their computation in terms of Kostka
numbers. The second main result is a simple and explicit combinatorial formula
for projecting product expansions in the quantum cohomology ring onto the sl(n)
Verlinde algebra. This projection is non-trivial and amounts to an identity
between numbers of rational curves intersecting Schubert varieties and
dimensions of moduli spaces of generalised theta-functions.
