Enumerating Large Orbits and Direct Condensation

Abstract

We describe a new algorithm for direct condensation, which is a tool in computational representation theory. The crucial point for this is the enumeration of very large orbits for a group acting on some set. We present a variation of the standard orbit enumeration algorithm that reduces the amount of storage needed and behaves well under parallelization. For the special case of matrices acting on a finite vector space an efficient implementation is described. This allows us to use condensation methods for considerably larger permutation representations than could be handled before.