FRG: Collaborative Research: Atlas of Lie Groups and Representations

American Institute Of Mathematics, Pasadena CA

Investigators

Abstract

Abstact Adams The problem of computing the set of irreducible unitary representations of a Lie group is one of the main unsolved problems in representation theory. The primary goal of this project 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, admissible representations, and unitary representations. Representation theory has applications to a broad spectrum of mathematical and scientific disciplines. Of particular significance is the central role it plays in modern number theory, automorphic forms and the Langlands program. On the other hand representation theory, in particular the study of unitary representations, is a very technical subject, and difficult for non-specialists. A primary goal of this project is to make information about Lie groups and representation accessible to a wide mathematical and scientific audience. Everything we do is being documented and made available through our web site, www.liegroups.org. This includes on-line tools for accessing information about representation theory. In addition we are developing a software package to do computations in structure theory, admissible representations, and unitary representations. This is comparable to the software package LiE for computing with semisimple Lie algebras, although at a considerably higher level. We envision this project playing a role in Lie groups comparable to the one the Atlas of Finite Groups plays in finite group theory.