Title page for ETD etd-1111102-110715


Type of Document Dissertation
Author Slay, David
URN etd-1111102-110715
Title Group Automorphisms and the Decomposition of Plancherel Measures
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Raymond Fabec Committee Chair
Ambar Sengupta Committee Member
Gestur Olafsson Committee Member
Lawrence Smolinsky Committee Member
Robert Lax Committee Member
John DiTusa Dean's Representative
Keywords
  • group automorphisms
  • decompostion of Plancherel measure
Date of Defense 2002-10-25
Availability unrestricted
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.

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