Harmonic Analysis on Semi-Simple Lie Groups I
The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie gr
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H erausgegeben von
J: L. Doob
. A. Grothendieck . E. Heinz· F. Hirzebruch E. Hopf· W. Maak . S. MacLane . W. Magnus· J. K. Moser M. M. Postnikov . F. K. Schmidt· D. S. Scott· K. Stein Geschiiftsfohrende H erausgeber
B. Eckmann und B. L. van der Waerden
Garth Warner
Harmonic Analysis on Semi-Simple Lie Groups I
Springer-Verlag Berlin Heidelberg New York 1972
Garth Warner Department of Mathematics, University of Washington Seattle, Washington
Geschäftsführende Herausgeber:
B. Eckmann Eidgenössische Technische Hochschule Zürich
B. L. van der Waerden Mathematisches Institut der Universität Zürich
AMS Subject Classifications (1970) 22 E45, 22 D 10,43 A 90,43 A 85,22 D 30
ISBN 978-3-642-50277-4 ISBN 978-3-642-50275-0 (eBook) DOI 10.1007/978-3-642-50275-0
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For Helen and Wyeth
Foreword The representation theory of locally compact groups has been vigorously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting certain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1.3.2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Examples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposition; a reference of the form A2.4, say, would mean the fourth number in the second appendix. Numbers in square brackets after an individual's name designate works in the Bibliography found at the end of the volume; a list of notational conventions can be found there too (
