Mathematical Sciences: Realization of Solvable Lie Groups inL 2 Cohomology Spaces and the Structure of Homogeneous      Domains in Cn
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{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
This project is mathematical research in the representation                theory of Lie groups.  A suitable example of the latter is the                  group of rotations of a sphere.  Groups like this are important                 because they occur in many areas of mathematics ( e.g. geometry,                differential equations, algebraic number theory, mathematical                   physics ) as groups of symmetries.  Representation theory allows                one to take advantage of symmetries in solving problems.                             More specifically, Professor Penney will explore how                       representation theory impinges on fundamental questions in                      complex analysis and geometry.  One such question concerns the                  realization of representations in square integrable cohomology                  spaces.  This is related to the structure theory of unbounded                   homogeneous domains in complex n-space.  Other questions to be                  investigated include the relation of the spectrum of the Laplace                - Beltrami operator of a Koszul domain to the geometry of the                   domain, the solvability properties of such operators, and the                   boundary theory of harmonic functions on such domains.
{'FirstName': 'Richard', 'LastName': 'Penney', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Richard C Penney', 'EmailAddress': 'rcp@math.purdue.edu', 'NSF_ID': '000361566', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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