Computing Maximal Tori Using LiE and Mathematica

This paper describes an algorithm for computing maximal tori of the reductive centralizer of a nilpotent element of an exceptional complex symmetric space. It illustrates also a good example of the use of Computer Algebra Systems to help answer important questions in the field of pure mathematics. Such tori play a fundamental rôle in several problems such as: classification of nilpotent orbits of real Lie groups [13], description of admissible nilpotent orbits of real Lie groups [14], [15], [16], [17], classification of spherical nilpotent orbits [8], [9], determination of component groups of centralizers of nilpotents in symmetric spaces [7], [10].