This book offers a systematic treatment--the first in book
form--of the development and use of cohomological induction to
construct unitary representations. George Mackey introduced
induction in 1950 as a real analysis construction for passing from
a unitary representation of a closed subgroup of a locally compact
group to a unitary representation of the whole group. Later a
parallel construction using complex analysis and its associated
co-homology theories grew up as a result of work by Borel, Weil,
Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological
induction, introduced by Zuckerman, is an algebraic analog that is
technically more manageable than the complex-analysis construction
and leads to a large repertory of irreducible unitary
representations of reductive Lie groups.
The book, which is accessible to students beyond the first year
of graduate school, will interest mathematicians and physicists who
want to learn about and take advantage of the algebraic side of the
representation theory of Lie groups. "Cohomological Induction and
Unitary Representations" develops the necessary background in
representation theory and includes an introductory chapter of
motivation, a thorough treatment of the "translation principle,"
and four appendices on algebra and analysis.
General
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