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＜電子ブック＞
Symmetry Breaking for Representations of Rank One Orthogonal Groups II / by Toshiyuki Kobayashi, Birgit Speh
(Lecture Notes in Mathematics. ISSN:16179692 ; 2234)

版	1st ed. 2018.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2018
大きさ	XV, 344 p. 15 illus., 11 illus. in color : online resource
著者標目	*Kobayashi, Toshiyuki author Speh, Birgit author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Topological groups LCSH:Lie groups LCSH:Number theory LCSH:Geometry, Differential LCSH:Differential equations LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Mathematical Physics FREE:Topological Groups and Lie Groups FREE:Number Theory FREE:Differential Geometry FREE:Differential Equations FREE:Global Analysis and Analysis on Manifolds
一般注記	1 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 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 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 HTTP:URL=https://doi.org/10.1007/978-981-13-2901-2

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