By Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner
This paintings is the 1st systematic examine of all attainable conformally covariant differential operators remodeling differential kinds on a Riemannian manifold X into these on a submanifold Y with concentrate on the version space (X, Y) = (Sn, Sn-1).
The authors provide a whole class of all such conformally covariant differential operators, and locate their specific formulæ within the flat coordinates when it comes to easy operators in differential geometry and classical hypergeometric polynomials. ensuing households of operators are traditional generalizations of the Rankin–Cohen brackets for modular varieties and Juhl's operators from conformal holography. The matrix-valued factorization identities between all attainable combos of conformally covariant differential operators also are established.
The major equipment of the evidence depends on the "F-method" lately brought and built through the authors. it's a basic technique to build intertwining operators between C∞-induced representations or to discover singular vectors of Verma modules within the context of branching ideas, as options to differential equations at the Fourier rework aspect. The e-book supplies a brand new extension of the F-method to the matrix-valued case within the basic atmosphere, that could be utilized to different difficulties as well.
This ebook deals a self-contained advent to the research of symmetry breaking operators for infinite-dimensional representations of reductive Lie teams. this option could be necessary for lively scientists and available to graduate scholars and younger researchers in differential geometry, illustration thought, and theoretical physics.
Read or Download Conformal Symmetry Breaking Operators for Differential Forms on Spheres (Lecture Notes in Mathematics) PDF
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