Conformal symmetry breaking operators for differential forms on spheres
Abstract
We give a complete classification of conformally covariant differential operators between the spaces of -forms on the sphere and -forms on the totally geodesic hypersphere . Moreover, we find explicit formul{\ae} for these new matrix-valued operators in the flat coordinates in terms of basic operators in differential geometry and classical orthogonal polynomials. We also establish matrix-valued factorization identities among all possible combinations of conformally covariant differential operators. The main machinery of the proof is the "F-method" based on the "algebraic Fourier transform of Verma modules" (Kobayashi-Pevzner [Selecta Math. 2016]) and its extension to matrix-valued case developed here. A short summary of the main results was announced in [C. R. Acad. Sci. Paris, 2016].
Cite
@article{arxiv.1605.09272,
title = {Conformal symmetry breaking operators for differential forms on spheres},
author = {Toshiyuki Kobayashi and Toshihisa Kubo and Michael Pevzner},
journal= {arXiv preprint arXiv:1605.09272},
year = {2016}
}