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OverviewThis 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 restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics.The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings.In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations.Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formulæ of these operators are also established.This book offers a self-contained and inspiring introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in representation theory, automorphic forms, differential geometry, and theoretical physics. Full Product DetailsAuthor: Toshiyuki Kobayashi , Birgit SpehPublisher: Springer Verlag, Singapore Imprint: Springer Verlag, Singapore Edition: 1st ed. 2018 Volume: 2234 Weight: 0.551kg ISBN: 9789811329005ISBN 10: 9811329001 Pages: 344 Publication Date: 28 December 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Introduction.- 2 Review of principal series representations.- 3 Symmetry breaking operators for principal series representations --general theory.- 4 Symmetry breaking for irreducible representations with infinitesimal character p.- 5 Regular symmetry breaking operators.- 6 Differential symmetry breaking operators.- 7 Minor summation formul related to exterior tensor i(Cn).- 8 More about principal series representations.- 9 Regular symmetry breaking operators eAi;j;;from I(i; ) to J (j; ).- 10 Symmetry breaking operators for irreducible representations with innitesimal character p.- 11 Application I.- 12 Application II.- 13 A conjecture.- 14 Appendix I.- 15 Appendix II.- List of Symbols.- Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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