A necessary and sufficient condition for irreducibility of parabolic baby Verma modules of sl(4,k)

Let G=SL(4,k) be a connected algebraic group over an algebraically closed field k of prime characteristic p and g=Lie(G)=sl(4,k). In this paper, we study representations of g with a p-character χ of standard Levi form. A necessary and sufficient condition for irreducibility of standard parabolic baby Verma g-modules is obtained.