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In this paper we classify and construct differential symmetry breaking operators \(\mathbb {D}\) from a line bundle over the real projective space \(\mathbb {R}\mathbb {P}^n\) to a vector bundle over \(\mathbb {R}\mathbb {P}^{n-1}\) . We further determine the factorization identities of \(\mathbb {D}\) and the branching laws of the corresponding generalized Verma modules of \(\mathfrak {sl}(n+1,\mathbb {C})\) . By utilizing the factorization identities, the \(SL(n,\mathbb {R})\) -representations realized on the image \(\textrm{Im}(\mathbb {D})\) are also investigated.

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Differential Symmetry Breaking Operators from a Line Bundle to a Vector Bundle over Real Projective Spaces

  • 会议论文

  • 发表日期：

    2026年

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  • Toshihisa Kubo

摘要

In this paper we classify and construct differential symmetry breaking operators \(\mathbb {D}\) from a line bundle over the real projective space \(\mathbb {R}\mathbb {P}^n\) to a vector bundle over \(\mathbb {R}\mathbb {P}^{n-1}\) . We further determine the factorization identities of \(\mathbb {D}\) and the branching laws of the corresponding generalized Verma modules of \(\mathfrak {sl}(n+1,\mathbb {C})\) . By utilizing the factorization identities, the \(SL(n,\mathbb {R})\) -representations realized on the image \(\textrm{Im}(\mathbb {D})\) are also investigated.