Classification of differential symmetry breaking operators for differential forms

Abstract : We give a complete classification of conformally covariant differential operators between the spaces of differential i-forms on the sphere S n 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 formulae for these matrix-valued operators in the flat coordinates and find factor-ization identities for them.
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Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner. Classification of differential symmetry breaking operators for differential forms. Comptes Rendus Mathématique, Elsevier Masson, 2016, 354 (7), pp.671 - 676. 〈10.1016/j.crma.2016.04.012〉. 〈hal-01907208〉

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