Collected Papers of Yozo Matsushima

Series in Pure Mathemati Collected Papers of Yozo Matsushima World Scientific This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank Collected Papers of Yoz6 Matsushima Published by World Scientific Publishing Co. Pie. Ltd. P O Box 128, Farrer Road, Singapore 9128 USA office: Suiie IB, 1060 Main Street, River Edge, NJ 07561 UK office: 73 Lynton Mead, Totteridge, London N20 SDH While every effort has been made ro contact the publishers of reprinted papers prior to publication, we have not been successful in a few cases. Where we could not contact the publishers, we have acknowledged the source of the material. Proper credit will be given to these publishers in future editions of this wort after permission is granted. COLLECTED PAPERS OF YOZO MATSUSHIMA Copyright © 1992 by World Scientific Publishing Co. Pie. Lid. Alt rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopy ing, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. ISBN 981-02-0814-6 Printed in Singapore by JBW Printers & Binders Pte. Ltd. Series in Pure Mathematics - Volume 15 Collected Papers of Yozo Matsushima Ifcfe World Scientific Singapore • New Jersey • London • Hong Kong V Yozo MATSUSHIMA 1921-1983 On April 9, 1983, Yozo Matsushima, professor of Osaka University, suc• cumbed to pneumonia in Osaka at the age of 62 years. His premature death produced no small effect among his colleagues and friends, and thus we would like to recall here the history of his life as it relates to the mathematical com• munity. Born on February 11, 1921 in Sakai City, Osaka Prefecture, he received his early education at the former Naniwa High School. In September 1942, he received his Bachelor of Science in mathematics from Osaka Imperial Univer• sity and immediately became an assistant in the Faculty of Science at the then newly established Nagoya Imperial University. Thus began Ills career as a mathematician. Within a short time, he was promoted to associate professor and in 1953 to full professor at Nagoya University. In the spring of 1960, he became a professor of Osaka University as successor to the chair of the late Kenjiro Shoda, who had been his former teacher and was at that time president of Osaka Uni• versity. During his professorship there, he was instrumental in organizing the mathematics department. Also at his suggestion and through his help, the Osaka Mathematical Journal and the Journal of Mathematics, Osaka City Uni• versity, were combined within a single publication, the Osaka Journal of Math• ematics. In September of 1966, he became professor at the University of Notre Dame, in Notre Dame, Indiana in the U.S. and remained so for fourteen years. In the summer of 1980, he returned to the Faculty of Science at Osaka Uni• versity. Before going to Notre Dame, Matsushima had been recognized not only in Japan, but also abroad, as is evidenced in the following events. In Sep• tember of 1954, he spent one year in France, at the Universities of Strasbourg and of Paris, where he had been invited by C.N.R.S. From September of 1962, he studied for one year at the Institute for Advanced Study in Princeton, New Jersey. In the fall of 1965 he returned to France where he was visiting professor at the University of Grenoble for one year. In the summer of 1965, he organized the U.S.-Japan Seminar on Differential Geometry together with Kentaro Yano and Katsumi Nomizu at the Research Institute for Mathematical Sciences at Kyoto University. This was the first international congress in Japan for geometers, and eleven mathematicians from the United States par• ticipated. Reprinted from Osaka J. Math. <1) 21 (1984). vi In 1962, Matsushima received the coveted Asahi Prize for his "Research of Continuous Groups". In 1967 he became a member of the first editorial board of the then newly established Journal of Differential Geometry and re• mained one of its editors throughout his lifetime. In May of 1980, prior to Matsushima's return to Osaka University, some fifty of his colleagues, former and present, showed their appreciation and respect for him by their participation in a conference in geometry held in his honor at the University of Notre Dame. In honor of his sixtieth birthday in February of 1981, a volume of papers was dedicated to Matsushima. Besides those papers written by his former students and colleagues especially for this occasion, some of the works presented at the above mentioned conference were also included in the volume which is entitled "Manifolds and Lie Groups, Papers in Honor of Yozo Matsushima", edited by J. Hano et al. and published by Birkhauser. As is outlined comprehensively in the following article generously con• tributed by Professor Shoshichi Kobayashi, in Matsushima's many mathematical works the emphasis is on the theory of Lie groups and manifolds. His works on these theories and on related topics such as discrete groups, unitary representa• tions, and functions of several complex variables have already proven to be valuable references in many current papers. Matsushima's love for mathematics is evidenced by the discipline and diligence he consistently applied to his research. He was a man whose con• cern lay not only in mathematics, but he had a keen interest in human nature and a constant curiosity about the world that resulted in his being an avid reader of a variety of books and a most interesting conversationalist. His friends and colleagues will miss not only his mathematical talent, but the warmth and cy• nical humour which lay behind his outwardly serious countenance. Shingo MURAKAMI vii Contents Yozo Mateushima (1921-1983) v S. Murakami The mathematical work of Y. Matsushima and its development 1 S. Kobayashi Bemerkungen iiber die Liesche Ringe mit Primzahlcharakteristik 18 Uber die multiplikative Gruppen einer p-adischen Divisionalgebra 21 (with T. Nakayama) Note on the replicas of matrices 28 On the Cartan decomposition of a Lie algebra 36 On algebraic Lie groups and algebras 39 On the faithful representations of Lie groups 51 On the decomposition of an (L)-group 59 On a type of subgroups of a compact Lie group 70 On the discrete subgroups and homogeneous spaces of nilpotent Lie groups 85 Some remarks on the exceptional simple Lie group S4 101 On a theorem concerning the prolongation of a differential system 107 Sur le prolongement d'un pseudogroupe d'isomorphismes locaux d'une variete differentiable 123 Sur les algebres de Lie lineaire semi-involutives 131 Pseudo-group es de Lie transitifs 148 Un theoreme sur les espaces homogenes complexes 162 Sur les espaces homogenes kahleriens d'un groupe de Lie reductif 164 Some studies on Kaehlerian homogeneous spaces 172 (with Hand) Sur la structure du groupe d'homeomorphismes analytiques d'une certaine variete kaehlerinne 188 Fibres holomorphes sur un tore complexe 194 viii Sur certains espaces fibres holomorphes sur une variete de Stein 218 (with A. Morimoto) Espaces homogenes de Stein des groupes de Lie complexes 237 Sur certaines varietes homogenes complexes 251 Espaces homogenes de Stein des groupes de Lie complexes, H 263 On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces 275 On Betti numbers of compact, locally symmetric Riemannian manifolds 294 On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds 314 (with S. Murakami) On the cohomology groups attached to certain vector valued differential forms on the product of the upper half-planes 366 (with G. Shimura) On the cohomology groups of locally symmetric, compact Riemannian manifolds 399 On certain cohomology groups attached to Hermitian symmetric spaces 405 (with S- Murakami) On certain cohomology groups attached to Hermitian symmetric spaces 440 (with S. Murakami) A formula for the Betti numbers of compact locally symmetric Riemannian manifolds 453 Affine structures on complex manifolds 464 On certain cohomology groups attached to Hermitian symmetric spaces (II) 472 Holomorphic vector fields and the first Chern class of a Hodge manifold 491 On the automorphisms and equivalences of generalized Siegel domains 495 (with W. Kaup and T. Ochiai) On automorphisms and equivalences of Siegel domains 519 Vector bundle valued harmonic forms and immersions of Riemannian manifolds 428 On Hodge manifolds with zero first Chern class 441 On the tube domains 448 Remarks on KahleT-Einstein manifolds 464 Ample vector bundles on compact complex spaces 477 (with W. Stoll) ix Holomorphic immersions of a compact Kahler manifold into complex tori 514 Weakly ample vector bundles and submanifolds of complex tori 534 (with A. Howard) On a problem of Stoll concerning a cohomology map from a flag manifold into a Grassmann manifold 574 Heisenberg groups and holomorphic vector bundles over a complex torus 613 On the intermediate cohomology group of a holomorphic line bundle over a complex torus 648 List of publications 663 List of Ph.D. theses written under the supervision of Yozo Matsushima 667 This page is intentionally left blank 1 The mathematical work of Y. Matsushima and its development Shoshichi KOBAYASHI*' In the past thirty years, differentia] geometry has undergone an enormous change with infusion of topology, Lie theory, complex analysis, algebraic ge• ometry and partial differential equations. Professor Matsushima played a leading role in this transformation by bringing new techniques of Lie groups and Lie algebras into the study of real and complex manifolds. He was a man of great insight; the problems he has worked on and the results he has obtained continue to be sources of inspiration for us geometers.

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