Simplicity conjecture for the theta-divisor variations

Let $(X,\Theta)$ be a principally polarized abelian variety over $\mathbb C$ of dimension $g\geq 2$ with smooth symmetric theta divisor $\Theta$. For $x\in X(\mathbb C)$, set

$$Y_x=\Theta_x\cap\Theta_{-x},$$

where $\Theta_x=\Theta+x$, and let

$$H=H^{g-2}(Y_x,\mathbb Q)/H^{g-2}(X,\mathbb Q)=H_+\oplus H_-$$

be the decomposition induced by the involution $\sigma=-\operatorname{id}_X$. The eigenspaces $H_\pm$ are the fibres of variations $\mathcal V_\pm$ of $\mathbb Q$-Hodge structures. Simplicity conjecture for the theta-divisor variations. If $\Theta$ is smooth, then $\mathcal V_\pm$ are simple. The simplicity of these variations is posed as part of the study of the varying Hodge structures of the intersections of translated theta divisors; the source provides no evidence of a resolution.