Symmetry Breaking for Representations of R...

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Beschreibung

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.

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.

Zusammenfassung

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 (Sn, Sn-1})

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xv 344 S. 4 s/w Illustr. 11 farbige Illustr. 344 p. 15 illus. 11 illus. in color.
ISBN-13:	9789811329005
ISBN-10:	9811329001
Sprache:	Englisch
Herstellernummer:	978-981-13-2900-5
Einband:	Kartoniert / Broschiert
Autor:	Speh, Birgit Kobayashi, Toshiyuki
Auflage:	1st edition 2018
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 20 mm
Von/Mit:	Birgit Speh (u. a.)
Erscheinungsdatum:	28.12.2018
Gewicht:	0,546 kg