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 λ − ρ, which have weight s γ λ − ρ for certain positive non-isotropic roots γ. This implies the existence of a nonzero homomorphism between the corresponding Verma modules.2010 Mathematics Subject Classification. Primary 17B10.

Odd Singular Vector Formula for General Linear Lie Superalgebras

“…Serganova [Se96] showed earlier the Hom space in (1) is non-vanishing by some indirect argument. We note that formulae for various singular vectors associated to an even reflection in a Verma module of a basic Lie superalgebra were recently established in [Sa17]; cf. also [CW17].…”