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