LEADER 04463nam 22007095 450 001 996466756503316 005 20200706163823.0 010 $a981-10-2657-2 024 7 $a10.1007/978-981-10-2657-7 035 $a(CKB)3710000000909303 035 $a(DE-He213)978-981-10-2657-7 035 $a(MiAaPQ)EBC5596111 035 $a(PPN)196319226 035 $a(EXLCZ)993710000000909303 100 $a20161011d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConformal Symmetry Breaking Operators for Differential Forms on Spheres$b[electronic resource] /$fby Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (IX, 192 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2170 300 $aIncludes index. 311 $a981-10-2656-4 330 $aThis work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin?Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C?-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2170 606 $aDifferential geometry 606 $aTopological groups 606 $aLie groups 606 $aMathematical physics 606 $aFourier analysis 606 $aPartial differential equations 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aDifferential geometry. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aMathematical physics. 615 0$aFourier analysis. 615 0$aPartial differential equations. 615 14$aDifferential Geometry. 615 24$aTopological Groups, Lie Groups. 615 24$aMathematical Physics. 615 24$aFourier Analysis. 615 24$aPartial Differential Equations. 676 $a515.7242 700 $aKobayashi$b Toshiyuki$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721059 702 $aKubo$b Toshihisa$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPevzner$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466756503316 996 $aConformal Symmetry Breaking Operators for Differential Forms on Spheres$91964424 997 $aUNISA