Symplectic Resolutions for Coverings of Nilpotent Orbits

Let $\text{0}$ be a nilpotent orbit in a semisimple complex Lie algebra $\text{g}$. Denote by $G$ the simply connected Lie group with Lie algebra $\text{g}$. For a $G$-homogeneous covering $M\to \text{0}$, let $X$ be the normalization of $\bar{\text{0}}$ in the function field of $M$. In this note, we study the existence of symplectic resolutions for such coverings $X$.