LEADER 04129nam a2200397 i 4500 001 991003633589707536 006 m o d 007 cr cn|---||||| 008 190328s2018 si a ob 001 0 eng d 020 $a9789811329012$q(electronic bk.) 020 $a981132901X$q(electronic bk.) 024 7 $a10.1007/978-981-13-2901-2 035 $ab14363458-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 0 $a516.1$223 100 1 $aKobayashi, Toshiyuki$0721059 245 10$aSymmetry breaking for representations of rank one orthogonal groups II$h[e-book] /$cToshiyuki Kobayashi, Birgit Speh 264 1$aSingapore :$bSpringer,$c2018 300 $a1 online resource (xv, 344 pages) :$billustrations (some color) 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2234 504 $aIncludes bibliographical references and index 505 0 $a1 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 520 $aThis work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup. The study of symmetry breaking operators (intertwining operators for restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics. The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings. In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations. Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formulæ of these operators are also established. This book offers a self-contained and inspiring introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in representation theory, automorphic forms, differential geometry, and theoretical physics 650 0$aBroken symmetry (Physics) 650 0$aGroup theory 650 0$aMathematical Physics 700 1 $aSpeh, Birgit$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0766106 856 40$zA book accessible through the World Wide Web$uhttp://link.springer.com/10.1007/978-981-13-2901-2 907 $a.b14363458$b03-03-22$c28-03-19 912 $a991003633589707536 996 $aSymmetry breaking for representations of rank one orthogonal groups II$91558274 997 $aUNISALENTO 998 $ale013$b28-03-19$cm$d@ $e-$feng$gsi $h0$i0