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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.
Next: Algebraic Geometry
Up: Lie Theory
Previous: Reflection Groups [HB 85]