Algorithms for Computing Restricted Root Systems and Weyl Groups

Abstract

While the computational packages LiE, Gap4, Chevie, and Magma are sufficient for work with Lie Groups and their corresponding Lie Algebras, no such packages exist for computing the k-structure of a group or the structure of symmetric spaces. My goal is to examine the k-structure of groups and the structure of symmetric spaces and arrive at various algorithms for computing in these spaces.