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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