Award Abstract #0532393
Atlas of Lie Groups

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	May 12, 2005
Latest Amendment Date:	May 12, 2005
Award Number:	0532393
Award Instrument:	Standard Grant
Program Manager:	Joe W. Jenkins DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	July 1, 2005
Expires:	June 30, 2008 (Estimated)
Awarded Amount to Date:	$118145
Investigator(s):	Jeffrey Adams jda@math.umd.edu (Principal Investigator)
Sponsor:	University of Maryland College Park 3112 LEE BLDG COLLEGE PARK, MD 20742 301/405-6269
NSF Program(s):	ANALYSIS PROGRAM
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,0000
Program Element Code(s):	1281

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.

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