Centraliser of $\Delta U$ in $U\otimes U$

Question

Let $U$ be a universal enveloping algebra of a simple Lie algebra $\mathfrak{g}$ over $\mathbb{C}$. What is a good reference for the centralizer of $\Delta (\mathfrak{g})$ in $U \otimes U$ ? Here $\Delta$ is the usual coproduct, the diagonal.