Symplectic Resolutions for Coverings of Nilpotent Orbits

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