We construct and give a complete classification of all the differential symmetry breaking operators [Formula: see text], between the spaces of smooth sections of a vector bundle of rank [Formula: see text] over the [Formula: see text]-sphere [Formula: see text], and a line bundle over the [Formula: see text]-sphere [Formula: see text]. In particular, we give necessary and sufficient conditions on the tuple of parameters [Formula: see text] for which these operators exist.

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