Group automorphisms and the decomposition of Plancherel measures

Identifier

etd-1111102-110715

Author

David Slay, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this paper, a natural action of the automorphisms of a group on the space of irreducible unitary representations is used to decompose the Plancherel measure on the dual space as an integral of measures on homogeneous spaces. Explicit decompositions are obtained for the cases of free 2 and 3-step nilpotent Lie groups. These results are obtained using direct integral decompositions, induced representations, the Mackey Machine, and measure theory on homogeneous spaces.

Date

2002

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Slay, David, "Group automorphisms and the decomposition of Plancherel measures" (2002). LSU Doctoral Dissertations. 3670.
https://repository.lsu.edu/gradschool_dissertations/3670

Committee Chair

Raymond Fabec

DOI

10.31390/gradschool_dissertations.3670