Construction and classification of differential symmetry breaking operators for principal series representations of the pair (SO₀ (4, 1), SO₀ (3, 1) ) for special parameters

Key Points

• Differential symmetry breaking operators are fully classified, bridging different spaces of vector bundles and line bundles.
• Operators map smooth sections from a vector bundle over the 3-sphere to a line bundle over the 2-sphere, specifically for |m| = N.
• The classification includes all possible parameters for the principal series representations of the groups involved.
• These findings may enhance the understanding of symmetry breaking phenomena in mathematical physics.