Highlights in Lie Algebraic Methods
An outgrowth of a two-week summer session at Jacobs University in Bremen, Germany in August 2009 ("Structures in Lie Theory, Crystals, Derived Functors, Harish–Chandra Modules, Invariants and Quivers"), this volume consists of expository and res
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Series Editors Hyman Bass Joseph Oesterlé Yuri Tschinkel Alan Weinstein
Anthony Joseph r Anna Melnikov r Ivan Penkov Editors
Highlights in Lie Algebraic Methods
Editors Anthony Joseph Department of Mathematics Weizmann Institute Rehovot 76100 Israel [email protected]
Ivan Penkov School of Engineering and Science Jacobs University Bremen 28759 Germany [email protected]
Anna Melnikov Department of Mathematics University of Haifa Mt. Carmel, Haifa 31905 Israel [email protected]
ISBN 978-0-8176-8273-6 e-ISBN 978-0-8176-8274-3 DOI 10.1007/978-0-8176-8274-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011940727 Mathematics Subject Classification (2010): 05C50, 05E15, 13F60, 14K05, 14L30, 14M17, 14M27, 16G70, 17B10, 15B36, 17B10, 17B22, 17B37, 17B55, 17B67, 17B99, 22E47 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.birkhauser-science.com)
Preface
A two-week Summer School on “Structures in Lie Theory, Crystals, Derived Functors, Harish-Chandra Modules, Invariants and Quivers” was held at Jacobs University Bremen during 9–22 August 2009 on both the geometric and algebraic aspects of Lie Theory. The participants were mainly from European countries with strong contingents from Germany, Russia, and Israel. Several high-level graduate courses were given, containing recent or original results on topics of particular current interest. The detailed notes of five of these lecture courses are reproduced in this volume. They not only provide a welcome reminder of the content of these courses to the participants, but enable all those who did not attend the meeting to profit from insights of leading specialists into the latest developments in some exciting fields of research. Even those participants who followed the courses attentively may profit from the details presented in this book. Besides the presenters of the graduate courses, some younger researchers were invited to speak at the meeting and to submit a manuscript for publication. Thus the present volume also contains five original articles. All the texts reproduced here were subject to a strict refereeing procedure befitting any mathematical journal.
The Courses Spherical Varieties by Michel Brion, Gre
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