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Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces (2408.01213v2)

Published 2 Aug 2024 in math.RT and math.DG

Abstract: 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 $\text{Im}(\mathbb{D})$ are also investigated.

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