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One of our results of this article is that every (projective) crepant resolution of a Slodowy slice in a nilpotent orbit closure in $mathfrak {sl}_N(mathbb C)$ can be obtained as the restriction of some crepant resolution of the nilpotent orbit closure. We also show that there is a decomposition of the Slodowy slice into other Slodowy slices with good properties. From this decomposition, one can count the number of crepant resolutions

Crepant Resolutions of a Slodowy Slice in a Nilpotent Orbit Closure in $\mathfrak {sl}_N(\mathbb C)$