Computing Maximal Tori Using LiE and Mathematica

摘要

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 role in several problems such as: classification of nilpotent orbits of real Lie groups, description of admissible nilpotent orbits of real Lie groups, classification of spherical nilpotent orbits, determination of component groups of centralizers of nilpotents in symmetric spaces.