This paintings is the 1st systematic research of all attainable conformally covariant differential operators reworking differential kinds on a Riemannian manifold X into these on a submanifold Y with specialise in the version space (X, Y) = (Sn, Sn-1).
The authors supply an entire type of all such conformally covariant differential operators, and locate their particular formulæ within the flat coordinates when it comes to easy operators in differential geometry and classical hypergeometric polynomials. ensuing households of operators are common generalizations of the Rankin–Cohen brackets for modular varieties and Juhl's operators from conformal holography. The matrix-valued factorization identities between all attainable mixtures of conformally covariant differential operators also are established.
The major equipment of the evidence will depend on the "F-method" lately brought and constructed by way of the authors. it's a basic approach 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 remodel facet. The e-book provides a brand new extension of the F-method to the matrix-valued case within the basic surroundings, that may be utilized to different difficulties as well.
This publication deals a self-contained advent to the research of symmetrybreaking operators for infinite-dimensional representations of reductive Lie teams. this option might be invaluable for lively scientists and obtainable to graduate scholars and younger researchers in differential geometry, illustration concept, and theoretical physics.
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