Atlas of Lie Groups

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The problem of computing the set of irreducible unitary representations ofa 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 particularwe plan to develop a set of software packages for computing structure theory ofLie groups and unitary representations.The impact of the project is addressed by our second goal, which is to makeinformation about Lie groups and representation theory accessible to the generalmathematical audience. This will be done through a web site which will containinteractive tools for accessing data about Lie groups and representations. Thesoftware we will develop will be publicly available, and provided with extensivedocumentation and a well designed user interface.The project will also have an impact on education by providing a mechanismfor new researchers to learn about the field and make contributions to it. In ad-dition, it will generate many mathematical and computational problems whichwill be tractable to non-experts, and will centralize and organize the state ofthe field to make it more accessible.We hope this project will have as much or more of an impact in Lie theoryas the Atlas of Finite Groups has in finite group theory.