Real Productive Groups I

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Academic Press, Mar 1, 1988 - Mathematics - 412 pages
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Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981.
This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology.
This book will be of interest to mathematicians and statisticians.
 

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Contents

Chapter 0 Background Material
1
Chapter 1 Elementary Representation Theory
17
Chapter 2 Real Reductive Groups
41
Chapter 3 The Basic Theory of g KModules
73
Chapter 4 The Asymptotic Behavior of Matrix Coefficients
107
Chapter 5 The Langlands Classification
137
Chapter 6 A Construction of the Fundamental Series
173
Chapter 7 Cusp Forms on G
225
Chapter 8 Character Theory
289
Chapter 9 Unitary Representations and g KCohomology
353
Bibliography
403
Index
411
Pure and Applied Mathematics
413
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