  We test the umbral methods introduced by Rota and Taylor within the theory of
representation of symmetric group. We define a simple bijection between the set
of all parking functions of length $n$ and the set of all noncrossing
partitions of $\{1,2,...,n\}$. Then we give an umbral expression of the
Frobenius characteristic of the parking function module introduced by Haiman
that allows an explicit relation between this symmetric function and the volume
polynomial of Pitman and Stanley.
