Groups of Lie Type [HB 86]

Changes:

• A much faster algorithm has been implemented for multiplication in groups of Lie type. This requires some preprocessing, so it may take longer to create such a group. The previous method is still available as an optional parameter. We can now compute the multiplicative Jordan decomposition of an element.

New features:

• The standard automorphisms of these groups are available (i.e. inner, diagonal, diagram, and field automorphisms). In many cases these give the full automorphism group.

• The highest weight representations of a group of Lie type can be computed--this gives all rational representations over the base field. The computation of the inverse of a representation of a group of Lie type over its base field can be achieved using GeneralisedRowReduction. We have a new function to compute the adjoint representation and a faster method for computing the standard representation.