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

Abstract: 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.