04465nam 22007095 450 991014897850332120200706163823.0981-10-2657-210.1007/978-981-10-2657-7(CKB)3710000000909303(DE-He213)978-981-10-2657-7(MiAaPQ)EBC5596111(PPN)196319226(EXLCZ)99371000000090930320161011d2016 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierConformal Symmetry Breaking Operators for Differential Forms on Spheres[electronic resource] /by Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner1st ed. 2016.Singapore :Springer Singapore :Imprint: Springer,2016.1 online resource (IX, 192 p.) Lecture Notes in Mathematics,0075-8434 ;2170Includes index.981-10-2656-4 This 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.Lecture Notes in Mathematics,0075-8434 ;2170Differential geometryTopological groupsLie groupsMathematical physicsFourier analysisPartial differential equationsDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Topological Groups, Lie Groupshttps://scigraph.springernature.com/ontologies/product-market-codes/M11132Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Differential geometry.Topological groups.Lie groups.Mathematical physics.Fourier analysis.Partial differential equations.Differential Geometry.Topological Groups, Lie Groups.Mathematical Physics.Fourier Analysis.Partial Differential Equations.515.7242Kobayashi Toshiyukiauthttp://id.loc.gov/vocabulary/relators/aut721059Kubo Toshihisaauthttp://id.loc.gov/vocabulary/relators/autPevzner Michaelauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910148978503321Conformal Symmetry Breaking Operators for Differential Forms on Spheres1964424UNINA