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We construct and give a complete classification of all the differential symmetry breaking operators \(\mathbb {D}_{\lambda , \nu }^{N,m}: C^\infty (S^3, \mathcal {V}_\lambda ^{2N+1}) \rightarrow C^\infty (S^2, \mathcal {L}_{m, \nu })\) , between the spaces of smooth sections of a vector bundle of rank \(2N+1\) over the 3-sphere \(\mathcal {V}_\lambda ^{2N+1} \rightarrow S^3\) , and a line bundle over the 2-sphere \(\mathcal {L}_{m, \nu } \rightarrow S^2\) in the special case \(|m| = N\) .

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Construction and Classification of Differential Symmetry Breaking Operators for Principal Series Representations of the Pair \((SO_0(4,1), SO_0(3,1))\) for Special Parameters

  • 会议论文

  • 发表日期：

    2026年

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  • Víctor Pérez-Valdés

摘要

We construct and give a complete classification of all the differential symmetry breaking operators \(\mathbb {D}_{\lambda , \nu }^{N,m}: C^\infty (S^3, \mathcal {V}_\lambda ^{2N+1}) \rightarrow C^\infty (S^2, \mathcal {L}_{m, \nu })\) , between the spaces of smooth sections of a vector bundle of rank \(2N+1\) over the 3-sphere \(\mathcal {V}_\lambda ^{2N+1} \rightarrow S^3\) , and a line bundle over the 2-sphere \(\mathcal {L}_{m, \nu } \rightarrow S^2\) in the special case \(|m| = N\) .