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We prove that a quotient singularity $\mathbb{C}^n/G $ by a finite subgroup$G\subset SL_n(\mathbb{C})$ has a crepant resolution only if $G $ is generatedby junior elements. This is a generalization of the result of Verbitsky [V]. Wealso give a procedure to compute the Cox ring of a minimal model of a given$\mathbb{C}^n/G$ explicitly from information of $G$. As an application, weinvestigate the smoothness of minimal models of some quotient singularities.Together with work of Bellamy and Schedler, this completes the classificationof symplectically imprimitive quotient singularities which admit projectivesymplectic resolutions.

On smoothness of minimal models of quotient singularities by finite subgroups of $SL_n(\mathbb{C})$