  It is shown that when dependence on the second flow of the KP hierarchy is
added, the resulting semi-stationary wave function of certain points in George
Wilson's adelic Grassmannian are generating functions of the exceptional
Hermite orthogonal polynomials. This surprising correspondence between
different mathematical objects that were not previously known to be so closely
related is interesting in its own right, but also proves useful in two ways: it
leads to new algorithms for effectively computing the associated differential
and difference operators and it also answers some open questions about them.
