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arXiv · 1605.05722

Classification of differential symmetry breaking operators for differential forms

Toshiyuki Kobayashi·Toshihisa Kubo·Michael Pevzner
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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 formul\ae{} for these matrix-valued operators in the flat coordinates and find factorization identities for them.

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Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner. 2016-05-18. Classification of differential symmetry breaking operators for differential forms. https://doi.org/10.1016/j.crma.2016.04.012.

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