Matrix Generators for Exceptional Groups of Lie Type

摘要

This paper gives a uniform method of constructing generators for matrix representations of inite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimension representation of an associated Lie algebra. These generators have been implemented in the computer algebra system Magma and this completes the provision of pairs of matrix generators for all finite groups of Lie type.