## Computating the Unitary Dual

This is the main page of a project to compute the unitary dual of
real, and some p-adic, semisimple groups. For more information,
including some expository papers on the subject, see
expository papers.
This is where you will find software related to the computation of the
unitary dual.
We are currently working on three aspects of this: models of Weyl
groups, structure theory of real groups, and spherical unitary
representations.

**Models of Representations of Weyl groups:**
See models, containing files with explicit matrices
for representations of Weyl groups, and some software.
Also see John Stembridge's site
Hereditary
Matrix Models for Weyl Groups for some tables and software.

**Spherical Unitary Representations of Split Groups**:
The results of
some computations, given as lists of spherical unitary
representations, may be found at spherical unitary representations.
Also see John Stembridge's
data
and
maple software.

**Structure Theory**: Currently under development by Fokko
du Cloux. This package will take the data for a real reductive group G
(a root datum plus some information about an involution) and give
structural information about G, including: toplogy, Cartan subgroups,
Weyl groups, parametrization of the admissible dual, and
Kazhdan--Lusztig--Vogan polynomials.

Here is the main page for the atlas software
package.

**Tables of Structure and Representation
Theory** for the exceptional groups. In particular you will find
information about all Cartan subgroups of all exceptional groups here.

Atlas Home Page