LEADER 03319nmm a2200445 i 4500 001 991003556219707536 007 cr cn ---mpcbr 008 161011s2016 si | o j |||| 0|eng d 020 $a9789811026560 024 7 $a10.1007/978-981-10-2657-7$2doi 035 $ab14351596-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a516.36$223 084 $aAMS 22E46 084 $aAMS 22E45 084 $aAMS 53A30 084 $aAMS 58J70 084 $aLC QA641-670 100 1 $aKobayashi, Toshiyuki$0721059 245 10$aConformal Symmetry Breaking Operators for Differential Forms on Spheres$h[e-book] /$cby Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner 260 $aSingapore :$bSpringer,$c2016 300 $a1 online resource (ix, 192 p.) 490 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2170 520 $aThis work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin?Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C?-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics 650 0$aTopological groups 650 0$aLie groups 650 0$aFourier analysis 650 0$aPartial differential equations 650 0$aDifferential geometry 650 0$aMathematical physics 700 1 $aKubo, Toshihisa$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0721058 700 1 $aPevzner, Michael 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9789811026560 856 40$uhttps://link.springer.com/book/10.1007/978-981-10-2657-7$zAn electronic book accessible through the World Wide Web 907 $a.b14351596$b03-03-22$c16-10-18 912 $a991003556219707536 996 $aConformal Symmetry Breaking Operators for Differential Forms on Spheres$91749148 997 $aUNISALENTO 998 $ale013$b16-10-18$cm$d@ $e-$feng$gsi $h0$i0