Award Abstract #0554278
FRG: Collaborative Research: Atlas of Lie Groups and Representations

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	April 26, 2006
Latest Amendment Date:	April 26, 2006
Award Number:	0554278
Award Instrument:	Standard Grant
Program Manager:	Joe W. Jenkins DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	June 1, 2006
Expires:	May 31, 2009 (Estimated)
Awarded Amount to Date:	$813471
Investigator(s):	Jeffrey Adams jda@math.umd.edu (Principal Investigator) Dan Barbasch (Co-Principal Investigator) David Vogan (Co-Principal Investigator) John Stembridge (Co-Principal Investigator) Fokko du Cloux (Co-Principal Investigator)
Sponsor:	American Institute of Mathematics 360 Portage Avenue Palo Alto, CA 94306 650/845-2071
NSF Program(s):	ANALYSIS PROGRAM
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,1616,0000
Program Element Code(s):	1281

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.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

(Showing: 1 - 6 of 6).

David Vogan.  "The character table for E8,"  Notices of the AMS,  2007, 

David Vogan.  "Representations of K,"  Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honour of Roger E. Howe (Lecture Note Series, Institute for Mathematical Sciences, National University of Singapor),  v.12,  2007, 

Jeffrey Adams.  "The Theta Correspondence over R,"  Harmonic = Analysis, Group Representations, Automorphic Forms and Invariant Theory: In Honour of Roger E. Howe (Institute for Mathematical Sciences, National University of Singapore),  v.12,  2007,  p. 1.

Peter Trapa.  "Leading-term cycles of Harish-Chandra modules and partial orders on components of the Springer fiber,"  Compositio Mathematicae,  v.143,  2007,  p. 515.

Peter Trapa and Hisayosi Matumoto.  "Derived functor modules arising as large constituents of degenerate principal series,"  Compositio Mathematicae,  v.143,  2007,  p. 222.

Wai Ling Yee.  "Signatures of Invariant Hermitian Forms on Irreducible Highest Weight Modules,"  Duke Mathematical Journal,  v.42,  2008,  p. 165-196.


(Showing: 1 - 6 of 6).

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