The purpose of these talks is to describe a concrete, explicitly computable, combinatorial description of G^. This has been implemented on computer by Fokko du Cloux. I will describe the algorithm itself, with some of the mathematical background. A separate session may be devoted to demonstrating the software.
Here is a little more detail about what the algorithm and software do. Suppose G is a connected, reductive, complex algebraic group, G(R) is a real form of G. Let K(R) be a maximal compact subgroup of G(R), with complexification K. The algorithm permits the following:
These work is part of the Atlas of Lie Groups and Representations, see the Atlas web site. One goal of the project is to compute the unitary dual of G(R). Another goal is to make this information and software available to the general mathematical audience. In particular an early version of the software may be downloaded at the Atlas software page.
For some background
reading for these talks see the papers section of the
atlas web site. In particular see
Combinatorics for the representation theory of real reductive groups
Parameters for Real Groups
Algorithms for Structure Theory