04129nam a2200397 i 4500991003633589707536m o d cr cn|---|||||190328s2018 si a ob 001 0 eng d9789811329012(electronic bk.)981132901X(electronic bk.)10.1007/978-981-13-2901-2b14363458-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng516.123Kobayashi, Toshiyuki721059Symmetry breaking for representations of rank one orthogonal groups II[e-book] /Toshiyuki Kobayashi, Birgit SpehSingapore :Springer,20181 online resource (xv, 344 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture notes in mathematics,0075-8434 ;2234Includes bibliographical references and index1 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 ; IndexThis 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 physicsBroken symmetry (Physics)Group theoryMathematical PhysicsSpeh, Birgitauthorhttp://id.loc.gov/vocabulary/relators/aut766106A book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-981-13-2901-2.b1436345803-03-2228-03-19991003633589707536Symmetry breaking for representations of rank one orthogonal groups II1558274UNISALENTOle01328-03-19m@ -engsi 0001243nam0 22003373i 450 CFI004590120231121125430.0IT81-10535 20140317d1981 ||||0itac50 baitaitz01i xxxe z01n˜Il œtempo del telefonol'insufficienza di EuclideLetizia Fabi De LauraRomaBulzoni1981238 p., \8! c. di tav.ill.21 cm.Biblioteca di cultura206001CFI00001562001 Biblioteca di cultura206TelefoniaStoriaFIRRMLC383604IServizi telefoniciStoriaFIRRMLC383605ITelefoniaAspetti socialiFIRRMLC411340I384.6Telefonia21Fabi De Laura, LetiziaCFIV0293240701440527ITIT-0120140317IT-FR0017 Biblioteca umanistica Giorgio ApreaFR0017 CFI0045901Biblioteca umanistica Giorgio Aprea 52MAG 6/751 52MAG0000131735 VMN RS A 2014031720140317 52Tempo del telefono3604609UNICAS