  Moments of the characteristic polynomial of a random matrix taken from any of
the three ensembles, orthogonal, unitary or symplectic, are given either as a
determinant or a pfaffian or as a sum of determinants. For gaussian ensembles
comparing the two expressions of the same moment one gets two remarkable
identities, one between an $n\times n$ determinant and an $m\times m$
determinant and another between the pfaffian of a $2n\times 2n$ anti-symmetric
matrix and a sum of $m\times m$ determinants.
