A lie subroutine for computing prehomogeneous spaces associated with complex nilpotent orbits

We develop a LiE subroutine to compute the irreducible components of certain prehomogeneous spaces that are associated with complex nilpotent orbits. An understanding of these spaces is necessary for solving more general problems in the theory of nilpotent orbits and the representation theory of Lie groups. The output is a set of ${\mbox\LaTeX}$ statements that can be compiled in a ${\mbox\LaTeX}$ environment in order to produce tables. Although the algorithm is used to solve the problem in the case of exceptional complex reductive Lie groups [2], it does describe these prehomogeneous spaces for the classical cases also. Complete tables for the exceptional groups can be found at http://www.math.umb.edu/~anoel/publications/tables/.