Conformal Symmetry Breaking Operators for Differential Forms on Spheres is popular PDF and ePub book, written by Toshiyuki Kobayashi in 2016-10-11, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Conformal Symmetry Breaking Operators for Differential Forms on Spheres can be Read Online from any device for your convenience.
Conformal Symmetry Breaking Operators for Differential Forms on Spheres Book PDF Summary
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.
Detail Book of Conformal Symmetry Breaking Operators for Differential Forms on Spheres PDF
- Author : Toshiyuki Kobayashi
- Release : 11 October 2016
- Publisher : Springer
- ISBN : 9789811026577
- Genre : Mathematics
- Total Page : 191 pages
- Language : English
- PDF File Size : 12,8 Mb
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