For a quasihereditary algebra $A$, we have a partially ordered set $\Lambda$ parameterizing the simples $L(\lambda)$/projectives indecomposables $P(\lambda)$. It also parameterize a set of special modules called the standard modules $\Delta(\lambda)$ such that $\Delta(\lambda) \to P(\lambda)$ is a surjection such that the kernel has composition factors $L(\mu)$ with $\mu > \lambda$ and $\Delta(\lambda)$ has composition factors with $L(\mu)$, for $\mu\leq \lambda$.
Now let $\Delta = \oplus_{\lambda\in\Lambda} \Delta(\lambda)$. Apparently, the following Ext-algebra: $\text{Ext}_A^\ast (\Delta,\Delta)$ is already known to be directed when $A$ is quasihereditary. Does anyone know the reference for this result and proof? Thanks.