Atlas of Lie Groups

University Of Maryland, College Park, College Park MD

Investigators

Abstract

The problem of computing the set of irreducible unitary representations of a Lie group is one of the main unsolved problems in representation theory. There are two primary goals of this proposal. The first goal is to compute the unitary dual of real and p-adic Lie groups, by a combination of mathematical and computational techniques. In particular we plan to develop a set of software packages for computing structure theory of Lie groups and unitary representations. The impact of the project is addressed by our second goal, which is to make information about Lie groups and representation theory accessible to the general mathematical audience. This will be done through a web site which will contain interactive tools for accessing data about Lie groups and representations. The software we will develop will be publicly available, and provided with extensive documentation and a well designed user interface. The project will also have an impact on education by providing a mechanism for new researchers to learn about the field and make contributions to it. In ad- dition, it will generate many mathematical and computational problems which will be tractable to non-experts, and will centralize and organize the state of the field to make it more accessible. We hope this project will have as much or more of an impact in Lie theory as the Atlas of Finite Groups has in finite group theory.