ON THE DUAL OF AN EXPONENTIAL SOLVABLE LIE GROUP (REPRESENTATION THEORY)

BRADLEY NORTON CURREY, Purdue University

Abstract

Let G be a connected, simply connected exponential solvable Lie group with Lie algebra g. The Kirillov mapping (eta):g*/Ad*(G) (--->) (')G gives a natural parameterization of (')G by co-adjoint orbits and is known to be continuous. The conjecture the (eta) is a homeomorphism has been open for some time. In this thesis a finite partition of g*/ Ad*(G) is defined by means of an explicit construction which gives the partition a natural total ordering, such that the minimal element is open and dense. Given (pi) (epsilon) (')G, elements in the enveloping algebra are constructed whose images under (pi) are scalar and give crucial information about the associated orbit. This information is then used to show that the restriction of (eta) to each element of the above mentioned partition is a homeomorphism.

Degree

Ph.D.

Subject Area

Mathematics

COinS