Singular vector formulas for Verma modules of simple Lie superalgebras

Abstract

For a simple Lie superalgebra of type BDFG, we give explicit formulas for singular vectors in a Verma module of highest weight $\lambda - \rho$, which have weight $s_{\gamma}\lambda - \rho$ for certain positive non-isotropic roots $\gamma.$ This implies the existence of a nonzero homomorphism between the corresponding Verma modules.