Induced nontrivial irreducible representations from H to G correspond bijectively to the G/H-quotient images of exceptional components in the minimal resolution of C^2/H.
Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Mathematics, 815
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Geometric Construction of the McKay-Slodowy Correspondence
Induced nontrivial irreducible representations from H to G correspond bijectively to the G/H-quotient images of exceptional components in the minimal resolution of C^2/H.