Matrix-Valued Factorization Identities
Differential symmetry breaking operators may be expressed as a composition of two equivariant differential operators for some special values of the parameters. Such formulæ in the scalar case are called “factorization identities” in [11] or “functional id
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Toshiyuki Kobayashi Toshihisa Kubo Michael Pevzner
Conformal Symmetry Breaking Operators for Differential Forms on Spheres
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Toshiyuki Kobayashi • Toshihisa Kubo Michael Pevzner
Conformal Symmetry Breaking Operators for Differential forms on Spheres
Toshiyuki Kobayashi Kavli IPMU and Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro, Tokyo, Japan
Toshihisa Kubo Ryukoku University Kyoto, Japan
Michael Pevzner Mathematics Laboratory, FR 3399 CNRS University of Reims-Champagne-Ardenne Reims, France
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-981-10-2656-0 ISBN 978-981-10-2657-7 (eBook) DOI 10.1007/978-981-10-2657-7 Library of Congress Control Number: 2016955062 Mathematics Subject Classification (2010): 22E47, 22E46, 53A30, 53C10, 58J70 © Springer Nature Singapore Pte Ltd. 2016 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 This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #22-06/08 Gateway East, Singapore 189721, Singapore
Contents
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Symmetry Breaking Operators and Principal Series Representations of G = O(n + 1, 1) . . . . . . . . . . . . . . . . . . . . . .
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