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Invariant Jacobians for irreducible restricted action

Abstract The problem of invariant Jacobians stems from the study of isolated singularities in complex geometry. In this paper, we deal with analogous problem of invariant Jacobians proposed by Stephen Yau in the case of prime characteristic. We give a complete classification of (infinitesimal version) invariant Jacobians for an irreducible action of the restricted Lie algebra . In particular, unlike the characteristic 0 case, the invariant Jacobians for irreducible actions may not be irreducible. We hope that it will be useful for the study of singularities in positive characteristic.