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.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8805712
Program Officer
William Y. Velez
Project Start
Project End
Budget Start
1988-06-01
Budget End
1991-11-30
Support Year
Fiscal Year
1988
Total Cost
$113,650
Indirect Cost
Name
Purdue Research Foundation
Department
Type
DUNS #
City
West Lafayette
State
IN
Country
United States
Zip Code
47907