
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
Springer (Publisher)
Published on 28. December 2018
Book
Paperback/Softback
XV, 342 pages
978-981-13-2900-5 (ISBN)
Description
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.
More details
Product info
Book
Series
Edition
2018
Language
English
Place of publication
Singapore
Singapore
Target group
Professional and scholarly
Illustrations
11 farbige Abbildungen, 4 s/w Abbildungen
4 schwarz-weiße und 11 farbige Abbildungen, Bibliographie
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 20 mm
Weight
546 gr
ISBN-13
978-981-13-2900-5 (9789811329005)
DOI
10.1007/978-981-13-2901-2
Schweitzer Classification
Other editions
Additional editions

Toshiyuki Kobayashi | Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
E-Book
12/2018
Springer
€48.14
Available for download
Content
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.