گروه‌های واقعی کاهشی I، جلد ۱۳۲ (ریاضیات خالص و کاربردی)

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. Sequel to "Real Reductive Groups I", this book emphasizes more analytical aspects of representation theory, but retains its focus on the interaction between algebra, analysis and geometry, like the first volume. The two volumes comprise a complete introduction to representation theory. 0.1.1. Let G be a locally compact topological group.