FRG: Collaborative Research: Atlas of Lie Groups and Representations

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AbstactAdamsThe problem of computing the set of irreducible unitaryrepresentations of a Lie group is one of the main unsolved problems inrepresentation theory. The primary goal of this project is to computethe unitary dual of real and p-adic Lie groups, by a combination ofmathematical and computational techniques. In particular we plan todevelop a set of software packages for computing structure theory ofLie groups, admissible representations, and unitary representations.Representation theory has applications to a broad spectrum ofmathematical and scientific disciplines. Of particular significance isthe central role it plays in modern number theory, automorphic formsand the Langlands program. On the other hand representation theory, inparticular the study of unitary representations, is a very technicalsubject, and difficult for non-specialists. A primary goal of thisproject is to make information about Lie groups and representationaccessible to a wide mathematical and scientific audience. Everythingwe do is being documented and made available through our web site,www.liegroups.org. This includes on-line tools for accessinginformation about representation theory. In addition we are developinga software package to do computations in structure theory, admissiblerepresentations, and unitary representations. This is comparable tothe software package LiE for computing with semisimple Lie algebras,although at a considerably higher level. We envision this projectplaying a role in Lie groups comparable to the one the Atlas of FiniteGroups plays in finite group theory.