

Here is a summary of the main features of the Atlas software.
Also see
See documenation on the atlas library,
and the files atlas.help and atlasfunctions.help in the atlasscripts directory.
The basics
 Complex reductive groups, root systems
 Real Reductive groups, inner classes and forms
 Maximal compact subgroup K(R) and its complexification K
 K orbits on G/B
 Langlands parameters
 Irreducible representations of K
 Branching to K
 KazhdanLusztigVogan polynomials
 Composition series and Character formulas
Hermitian Forms and unitarity
 Hermitian representations, invariant Hermitian forms
 The cinvariant form
 Signatures of forms
 Unitarity
 Jantzen filtration
Induction
 Parabolic subgroups, Levi subgroups
 Real parabolic induction and cohomological induction
Structure Theory
 Levi subgroups
 PseudoLevi subgroups
 Equal rank reductive subgroups and their poset
 Levi subgroups
The Weyl group
 The Weyl group W
 Conjugacy classes, characters of W
 Character table of W
 Representations of W
 Coherent Continuation
Nilpotent Orbits
 Nilpotent orbit of a complex group
 Nilpotent orbits of a real group
 Component group of centralizer of a nilpotent element
 Special nilpotent orbits
 Duality of nilpotent orbits
 Springer Correspondence
 Associated variety of ideals in the Universal enveloping algebra
 Gelfand Kirillov dimension
Lusztig's theory of the Weyl group
 Generic degree and fake degree
 cells of representations of the Weyl group
 Lusztig's parametrization of representations of W
Unipotent Representations
 Unipotent representations of a real reductive group
 Weak Arthur packets of unipotent representations
Miscellaneous
 structure constants
 The Tits group
 Extended groups
