Compactification of Symmetric Spaces
The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of
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Series Editors Hyman Bass Joseph Oesterle Alan Weinstein
Yves Guivarc'h Lizhen Ji J.C. Taylor
Compactifications of Symmetric Spaces
Birkhauser Boston • Basel • Berlin
Yves Guivarc'h IRMAR UFR Mathematiques Universite de Rennes-I Rennes, France
Lizhen Ji Department of Mathematics University of Michigan Ann Arbor, MI
J. C. Taylor Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada
Library of Congress Cataloging-in-Publication Data
Guivarc'h, Yves Compactifications of symmetric spaces / Yves Guivarc'h, Lizhen Ji, John C. Taylor. p. cm. -- (Progress in mathematics; v. 156) Includes bibliographical references (p. ) and index. ISBN-13: 978-1-4612-7542-8 e-ISBN-13: 978-1-4612-2452-5 DOl: 10.1007/978-1-4612-2452-5 1. Symmetric spaces. 2. Compactifications. I. Ji, Lizhen, 1964II. Taylor, J. C. (John Christopher), 1936- . III. Compactifications of Symmetric Spaces. IV. Series: Progress in Mathematics (Boston, Mass.); vol. 156 QA670.G85 1997 97-27755 516.3'62--dc21 CIP AMS Subject Classification: 53C35, 22E30, 51f15, 60145, 31C35, 43A85, 60150
Printed on acid-free paper Birkhduser © 1998 Birkhiiuser Boston Softcover reprint of the hardcover 1st edition 1998
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CONTENTS
Preface ............................................................ xi Chapter I. Introduction .......................................... 1 Statement of the main new results ................................ 2 Characterizations of the compactification X SF .................... 4 The Karpelevic compactification XK .............................. 6 Fibers of maps between the compactifications ..................... 6 Application to Brownian motion .................................. 8 Eigenfunctions and Martin's method .............................. 9 Methods of proof ................................................. 9 Open problems .................................................. 10 Conventions ..................................................... 12 Study guide .........................................
