Maximal subalgebras of Lie superalgebras of Cartan type over fields of characteristic zero

This paper aims to characterize the maximal graded subalgebras of Lie superalgebras of Cartan type W, S  , S˜ and H over fields of characteristic zero. All maximal graded subalgebras are completely determined by virtue of a constructive method and their isomorphism classes; dimension formulas are given except for maximal S-subalgebras. In the exceptional situation, the classification of maximal S-subalgebras is reduced to the classification of the maximal irreducible subalgebras for the classical Lie algebras.