NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF OKLAHOMA
Initial Amendment Date:	May 29, 1992
Latest Amendment Date:	May 29, 1992
Award Number:	9204488
Award Instrument:	Standard Grant
Program Manager:	Joe W. Jenkins DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	June 1, 1992
End Date:	May 31, 1995 (Estimated)
Total Intended Award Amount:	$38,552.00
Total Awarded Amount to Date:	$38,552.00
Funds Obligated to Date:	FY 1992 = $38,552.00
History of Investigator:	Tomasz Przebinda (Principal Investigator) tprzebinda@ou.edu
Recipient Sponsored Research Office:	University of Oklahoma Norman Campus 660 PARRINGTON OVAL RM 301 NORMAN OK  US  73019-3003 (405)325-4757
Sponsor Congressional District:	04
Primary Place of Performance:	DATA NOT AVAILABLE
Primary Place of Performance Congressional District:
Unique Entity Identifier (UEI):	EVTSTTLCEWS5
Parent UEI:
NSF Program(s):	MODERN ANALYSIS
Primary Program Source:
Program Reference Code(s):
Program Element Code(s):	126200
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Przebinda will investigate distribution characters and matrix coefficients of irreducible unitary representation of classical Lie groups from the viewpoint of microlocal analysis in the context of Howe's theory of reductive dual pairs, via the Cayley transform. Use will be made of Howe's theory, microlocal analysis, and Harish-Chandra's theory of orbital integrals to construct irreducible unitary representations of classical Lie groups, attached to nilpotent coadjoint orbits. This attachment occurs on three levels: associated varieties, wave front sets, and character formulas. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics. **//

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