Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Toshiyuki Kobayashi, Birgit Speh (Autoren)

Buch | Softcover

344 Seiten

2018 | 1st ed. 2018
Springer Verlag, Singapore
978-981-13-2900-5 (ISBN)

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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.

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.

Erscheinungsdatum	28.11.2018
Reihe/Serie	Lecture Notes in Mathematics ; 2234
Zusatzinfo	11 Illustrations, color; 4 Illustrations, black and white; XV, 344 p. 15 illus., 11 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	automorphic forms • Differential Geometry • fourier analysis • Gross-Prasad conjectures • infinite dimensional representations • Plancherel formulas • pseudo Riemannian symmetric space • Reductive Lie groups • Representation Theory • symmetry breaking operators
ISBN-10	981-13-2900-1 / 9811329001
ISBN-13	978-981-13-2900-5 / 9789811329005
Zustand	Neuware