By Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner
This paintings is the 1st systematic learn of all attainable conformally covariant differential operators reworking 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 particular formulæ within the flat coordinates when it comes to simple operators in differential geometry and classical hypergeometric polynomials. ensuing households of operators are common 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 via 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 principles, as options to differential equations at the Fourier remodel facet. The booklet supplies a brand new extension of the F-method to the matrix-valued case within the normal environment, that can be utilized to different difficulties as well.
This booklet deals a self-contained creation to the research of symmetry breaking operators for infinite-dimensional representations of reductive Lie teams. this selection might be useful for energetic scientists and available to graduate scholars and younger researchers in differential geometry, illustration conception, and theoretical physics.
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Additional info for Conformal Symmetry Breaking Operators for Differential Forms on Spheres (Lecture Notes in Mathematics)
Conformal Symmetry Breaking Operators for Differential Forms on Spheres (Lecture Notes in Mathematics) by Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner