This paintings is the 1st systematic examine of all attainable conformally covariant differential operators remodeling differential varieties 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 an entire type of all such conformally covariant differential operators, and locate their specific formulæ within the flat coordinates when it comes to simple operators in differential geometry and classical hypergeometric polynomials. ensuing households of operators are average generalizations of the Rankin–Cohen brackets for modular kinds 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 constructed through 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 recommendations to differential equations at the Fourier remodel aspect. The booklet provides a brand new extension of the F-method to the matrix-valued case within the basic surroundings, that could be utilized to different difficulties as well.
This ebook deals a self-contained advent to the research of symmetrybreaking operators for infinite-dimensional representations of reductive Lie teams. this selection may be necessary for lively scientists and obtainable to graduate scholars and younger researchers in differential geometry, illustration thought, and theoretical physics.
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