Implementation of Stanley’s algorithm for projective group imbeddings

Computing intersection cohomology Betti numbers is complicated by the fact that the usual long exact localization sequences in Borel–Moore homology do not carry over to the setting of intersection homology. Nevertheless, about 20 years ago, Richard Stanley had formulated a remarkable algorithm for computing the intersection cohomology Betti numbers of toric varieties. During the last few years, Michel Brion and the first author were able to extend this to a much larger class of spherical varieties. This algorithm has been implemented as an interactive script written for the programming package GAP (using also LiE and polymake) by the authors. This paper is an exposition of this implementation.