  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.
