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Lecture Notes in Mathematics

Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Authors: Kobayashi, Toshiyuki, Speh, Birgit

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  • Introduces a new method to construct and classify matrix-valued symmetry breaking operators in representation theory
  • Includes hot topics of automorphic forms and conformal geometry as applications of branching rules in representation theory
  • Provides the complete classification of all conformally equivariant operators on differential forms on the model space (S<i>n, Sn-1})
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About this book

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 (XY) = (SnSn-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.

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-981-13-2901-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-981-13-2900-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Symmetry Breaking for Representations of Rank One Orthogonal Groups II
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2234
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-2901-2
DOI
10.1007/978-981-13-2901-2
Softcover ISBN
978-981-13-2900-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XV, 344
Number of Illustrations
4 b/w illustrations, 11 illustrations in colour
Topics

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