The Grassmannian Variety Geometric and Representation-Theoretic Aspe
This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossr
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V. Lakshmibai Justin Brown
The Grassmannian Variety Geometric and Representation-Theoretic Aspects
Developments in Mathematics VOLUME 42 Series Editors: Krishnaswami Alladi, University of Florida, Gainesville, FL, USA Hershel M. Farkas, Hebrew University of Jerusalem, Jerusalem, Israel
More information about this series at http://www.springer.com/series/5834
V. Lakshmibai • Justin Brown
The Grassmannian Variety Geometric and Representation-Theoretic Aspects
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Justin Brown Department of Mathematics Olivet Nazarene University Bourbonnais, IL, USA
V. Lakshmibai Department of Mathematics Northeastern University Boston, MA, USA
ISSN 1389-2177 Developments in Mathematics ISBN 978-1-4939-3081-4 DOI 10.1007/978-1-4939-3082-1
ISSN 2197-795X (electronic) ISBN 978-1-4939-3082-1 (eBook)
Library of Congress Control Number: 2015947780 Mathematics Subject Classification (2010): 14M15, 14L24, 13P10, 14D06, 14M12 Springer New York Heidelberg Dordrecht London © Springer Science+Business Media New York 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www. springer.com)
Preface
This monograph represents an expanded version of a series of lectures given by V. Lakshmibai on Grassmannian varieties at the workshop on “Geometric Representation Theory” held at the Institut Teknologi Bandung in August 2011. While giving the lectures at the workshop, Lakshmibai realized the need for an introductory book on Grassmannian varieties that would serve as a good resource for learning about Grassmannian varieties, especially for graduate students as well as researchers who want to work in this area of algebraic geometry. Hence, the creation of this monograph. This book provides an introduction to Grassmannian varieties and their Schubert subvarieties, focusing on the treatment of geometric and representation theoretic aspects. After a brief discussion on the basics of commu
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