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.

arXiv commentversion 3, 16 pages, title change, to appear in J. Algebra