Mackey Bijection for some Reductive Groups and Continuous Fields of Reduced C*-Algebras
Open Access
Author:
Roman-Martinez, Angel
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
September 18, 2019
Committee Members:
Nigel David Higson, Dissertation Advisor/Co-Advisor Nigel David Higson, Committee Chair/Co-Chair Nathanial Patrick Brown, Committee Member Paul Frank Baum, Committee Member Murat Gunaydin, Outside Member Eyal Subag, Special Member Carina Pamela Curto, Program Head/Chair
Keywords:
Representation theory Mackey bijection Reduced group C*-algebra
Abstract:
The purpose of this dissertation is to make a further contribution to the Mackey bijection for a complex reductive group G and for SL(2,R), between the tempered dual of G and the unitary dual of the associated Cartan motion group. We shall construct an embedding of the C*-algebra of the motion group into the reduced C*-algebra of G, and use it to characterize the continuous field of reduced group C*-algebras that is associated to the Mackey bijection. We shall also obtain a new characterization of the Mackey bijection using the same embedding.
