Markman's monodromy conjecture for generalized Kummer varieties

Let $X$ be deformation equivalent to a generalized Kummer variety of dimension $2n$, with $n\geq 2$. Then $H^2(X,\mathbb Z)$ is isometric to $\Lambda:=U\oplus U\oplus U\oplus \mathbb Z\delta$, where $U$ is the unimodular rank-$2$ lattice of signature $(1,1)$ and $(\delta,\delta)=-2-2n$. For $u\in H^2(X,\mathbb Z)$ with $(u,u)=2$, set $\rho_u=-R_u$, and for $(u,u)=-2$, set $\rho_u:=R_u$. Let ${\mathcal N}(X)$ be the subgroup of $O^+[H^2(X,\mathbb Z)]$ generated by products $\rho_{u_1}\cdots\rho_{u_k}$ in which $(u_i,u_i)=-2$ for an even number of indices and $(u_i,u_i)=2$ for the remaining indices. Markman's monodromy conjecture. $Mon^2(X)={\mathcal N}(X)$. The source records the inclusion ${\mathcal N}(X)\subset Mon^2(X)$ as proved and the equality as known when $n=2$; the general equality remains unresolved there.