Award Abstract #0554278
FRG: Collaborative Research: Atlas of Lie Groups and Representations
NSF Org: |
DMS
Division of Mathematical Sciences
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Initial Amendment Date: |
April 26, 2006 |
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Latest Amendment Date: |
April 26, 2006 |
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Award Number: |
0554278 |
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Award Instrument: |
Standard Grant |
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Program Manager: |
Joe W. Jenkins
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences
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Start Date: |
June 1, 2006 |
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Expires: |
May 31, 2009 (Estimated) |
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Awarded Amount to Date: |
$813471 |
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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)
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Sponsor: |
American Institute of Mathematics
360 Portage Avenue
Palo Alto, CA 94306 650/845-2071
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NSF Program(s): |
ANALYSIS PROGRAM
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Field Application(s): |
0000099 Other Applications NEC
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Program Reference Code(s): |
OTHR,1616,0000
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Program Element Code(s): |
1281
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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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