Generation conjecture for invariant operators on symmetric tensor densities

Let $R_{\delta}$ be the space of symmetric tensor densities of weight $\delta$, decomposed into homogeneous components $R^k_{\delta}$, and let $X$ and $i(\alpha)$ denote the invariant operators acting on these spaces. The spaces $R^k_{\delta}$ have projectors onto them.

Generation conjecture. The algebra of all invariant operators for the $sp(2n+2)$ action on $R_{\delta}$ is generated by the operators $X$, $i(\alpha)$ and the projectors onto the spaces $R^k_{\delta}$.

This conjecture gives the expected $sl(2,\mathbb{R})$-module description of the invariant operators and underlies the proposed construction of projectors onto $R^k_{\delta}\capker\,i(\alpha) i(\alpha)$. The supplied text does not state whether the conjecture has been proved or disproved.