GAP4 package SLA
A GAP4 package for doing computations with various aspects
of the theory of simple Lie algebras (in characteristic 0).
Installation: just gunzip, and untar sla-xx.tar.gz
in the pkg directory; then,
in GAP, you can use LoadPackage( "sla" ); to load the package.
- Functions for working with the nilpotent orbits in a semisimple Lie
algebra (creation of sl2-triples, finding the weighted Dynkin diagram of a
given nilpotent element, finding the induced nilpotent orbits and the
- Functions for working with the orbits of a θ-group (listing of
the nilpotent orbits, determining the closure diagram, finding a Cartan
- A database of semisimple subalgebras, up to linear equivalence,
of semisimple Lie algebras of
ranks up to 8, and functions for working with it (creating a semisimple Lie
algebra and its subalgebras, computing the corresponding branching rules,
determining the inclusions between the subalgebras).
- A function for listing the closed subsets of a root system, up to the
action by the Weyl group.
- An implementation of Popov's algorithm for computing the characteristics
of the (Hesselink-) strata of the nullcone of an irreducible representation
of a semisimple algebraic group.
NOTE: this package needs the QuaGroup
For the latest version visit: