Classification of differential symmetry breaking operators for   differential forms
  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. 
Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner
math.DG math-ph math.MP math.RT