Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Nonfiction, Science & Nature, Mathematics, Group Theory, Science, Physics, Mathematical Physics
Cover of the book Symmetry Breaking for Representations of Rank One Orthogonal Groups II by Toshiyuki Kobayashi, Birgit Speh, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Toshiyuki Kobayashi, Birgit Speh ISBN: 9789811329012
Publisher: Springer Singapore Publication: December 27, 2018
Imprint: Springer Language: English
Author: Toshiyuki Kobayashi, Birgit Speh
ISBN: 9789811329012
Publisher: Springer Singapore
Publication: December 27, 2018
Imprint: Springer
Language: English

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) = (S**nSn-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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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) = (S**nSn-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 books from Springer Singapore

Cover of the book German-Australian Encounters and Cultural Transfers by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Hydrogels by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Calcium Signaling: From Physiology to Diseases by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Secure Networked Inference with Unreliable Data Sources by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Active Vibration Control and Stability Analysis of Flexible Beam Systems by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Social Democracy and the Crisis of Equality by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Philosophical Logic: Current Trends in Asia by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Information and Communication Technology for Intelligent Systems by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Cultural Conflict in Hong Kong by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Experimental Techniques in Host-Plant Resistance by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Telocytes by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Successful Transposition of Lesson Study by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Ravine Lands: Greening for Livelihood and Environmental Security by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Nutritional Anemia in Preschool Children by Toshiyuki Kobayashi, Birgit Speh
Cover of the book Information Technology and Applied Mathematics by Toshiyuki Kobayashi, Birgit Speh
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy