T. Kobayashi, T. Kubo, and M. Pevzner. Classification of differential symmetry breaking operators for differential forms. C. R. Acad. Sci. Paris, Ser.I, 354 (2016), pp. 671-676, 2016. published online 17 May 2016. DOI: 10.1016/j.crma.2016.04.012..

We give a complete classification of conformally covariant differential operators between the spaces of differential i-forms on the sphere Sⁿ and j-forms on the totally geodesic hypersphere S^n-1 by analyzing the restriction of principal series representations of the Lie group O(n+1,1). Further, we provide explicit formula for these matrix-valued operators in the flat coordinates and find factorization identities for them.

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© Toshiyuki Kobayashi