  We obtain the collection of symmetric and symplectic matrix integrals and the
collection of Pfaffian tau-functions, recently described by Peng and Adler and
van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector
of a fermionic Fock space. This fermionic Fock space is the same space as one
constructs to obtain the KP and 1-Toda lattice hierarchy.
