Symmetry Breaking for Representations of Rank One Orthogonal Groups II
This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.The study of symmetry breaking operators (intertwining operators for restri
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Toshiyuki Kobayashi Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Toshiyuki Kobayashi • Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
123
Toshiyuki Kobayashi Graduate School of Mathematical Sciences The University of Tokyo Komaba, Tokyo, Japan and Kavli IPMU Kashiwa, Japan
Birgit Speh Department of Mathematics Cornell University Ithaca, NY, USA
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-981-13-2900-5 ISBN 978-981-13-2901-2 (eBook) https://doi.org/10.1007/978-981-13-2901-2 Library of Congress Control Number: 2015027247 Mathematics Subject Classification (2010): 22E30, 11F70, 53A30, 22E45, 22E46, 58J70 © Springer Nature Singapore Pte Ltd. 2018 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
For a pair (G, G ) = (O(n + 1, 1), O(n, 1)) of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations Iδ (V , λ) of G and Jε (W, ν) of the subgroup G . The representations are parametrized by finite-dimensional representations V , W of O(n) respectively of O(n − 1), characters δ, ε of O(1), and λ, ν ∈ C. Denote by [V : W ] the multiplicity of W occurring
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