  We compute the characters of the simple GL-equivariant holonomic D-modules on
the vector spaces of general, symmetric and skew-symmetric matrices. We realize
some of these D-modules explicitly as subquotients in the pole order filtration
associated to the determinant/Pfaffian of a generic matrix, and others as local
cohomology modules. We give a direct proof of a conjecture of Levasseur in the
case of general and skew-symmetric matrices, and provide counterexamples in the
case of symmetric matrices. The character calculations are used in subsequent
work with Weyman to describe the D-module composition factors of local
cohomology modules with determinantal and Pfaffian support.
