Relations conjecture for invariant differential operators on the Siegel–Jacobi space

Let ${\mathscr P}_{n,m}$ be the Siegel–Jacobi space, and let $D_j$ for $1\leq j\leq n$ and $\Omega_{pq}^{(k)}$ for $0\leq k\leq n-1$ and $1\leq p\leq q\leq m$ be the invariant differential operators defined in the source. The relations (4.14), (4.15), and (4.16) are the commutation relations displayed immediately before the conjecture. Relations conjecture. These relations generate all relations among the set

$$\left\{D_j,\,\Omega_{pq}^{(k)}\mid 1\leq j\leq n,\ 0\leq k\leq n-1,\ 1\leq p\leq q\leq m\right\}.$$

This conjecture asserts that the displayed commutation relations give a complete presentation of the relations among the invariant differential operators. The supplied text gives no evidence that it has been resolved.