Maximal Subalgebras for Modular Graded Lie Superalgebras of Odd Cartan Type

The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic $p>3$. All maximal graded subalgebras consist of three types (MyRoman{1}), (MyRoman{2}) and (MyRoman{3}). Maximal graded subalgebras of type (MyRoman{3}) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (MyRoman{1}), (MyRoman{2}) and reducible maximal g raded subalgebras.The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra $mathfrak{p}(n)$.