Janzten coefficients and Blocks of category ${\mathcal{O}}^{\mathfrak{p}}$

The BGG category $\mathcal{O}$ and its generalization ${\mathcal{O}}^{\mathfrak{p}}$ play essential roles in representation theory and have led to far-reaching work. Some elementary problems remain open for several decades, such as the block decomposition of category ${\mathcal{O}}^{\mathfrak{p}}$. In this paper, we solve the problem of blocks by applying the theory of Jantzen coefficients.