Conformal Symmetry Breaking Operators for Differential Forms on Spheres

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Conformal Symmetry Breaking Operators for Differential Forms on Spheres

フォーマット:
電子ブック
責任表示:
by Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner
本文言語:
英語
出版情報:
Singapore, Singapore. 2016-. Springer Singapore,Imprint: Springer
シリーズ:
Lecture Notes in Mathematics; 2170
概要:
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. 続きを見る
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Extensions of Positive Definite Functions : Applications and Their Harmonic Analysis by Jorgensen, Palle; Pedersen, Steen; Tian, Feng; SpringerLink
2.
Analytic, Algebraic and Geometric Aspects of Differential Equations : Będlewo, Poland, September 2015 by Filipuk, Galina; Haraoka, Yoshishige; Michalik, Sławomir; SpringerLink
3.
Geometry and Topology of Manifolds : 10th China-Japan Conference 2014 by Futaki, Akito; Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping; SpringerLink
4.
Ricci Flow and Geometric Applications : Cetraro, Italy 2010 by Boileau, Michel; Besson, Gerard; Sinestrari, Carlo; Tian, Gang; Benedetti, Riccardo; Mantegazza, Carlo; SpringerLink
5.
Geometric Methods in PDE’s by Citti, Giovanna; Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco; SpringerLink
6.
Quantization, PDEs, and Geometry : The Interplay of Analysis and Mathematical Physics by Bahns, Dorothea; Bauer, Wolfram; Witt, Ingo; SpringerLink
7.
Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics by Colombini, Ferruccio; Del Santo, Daniele; Lannes, David; SpringerLink
8.
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