Nakajima's zero-weight-space conjecture for quiver varieties

Let $M_{0,\lambda}(d,v)$ be the quiver variety in question, and set

$$top=\frac{1}{2}\dim H_*(M_{0,\lambda}(d,v)).$$

Let $(L_d)_0$ denote the $0$-weight space of the Kac–Moody algebra associated to the quiver, for the representation of highest weight $\sum_i d_i\bar{\omega}_i$. Nakajima's zero-weight-space conjecture. There should be an isomorphism

$$H^{top}\bigl(M_{(0,\lambda)}(d,v),\mathbb C\bigr)\simeq (L_d)_0.$$

The conjecture is motivated by Nakajima's theorem and the canonical comparison between the relevant quiver varieties in the stated setting. The supplied text does not indicate whether it has been resolved.