Singular Vectors In Verma Modules For Lie Superalgebra Gl(3|1)

We introduce a method to compute the singular vectors in Verma modules for Lie su-peralgebra gl(3|1)when the highest weight of its Verma module is atypical.And a corollary also be given to decide whether a Verma module is simple.In the end,we calculate the super Weyl group of gl(1|2)such that all the simple root systems of gl(1|2)are conjugate under this super Weyl group.