Shapovalov determinants of Q-type Lie superalgebras

Abstract

We define an analogue of Shapovalov forms for <it>Q</it>-type Lie superalgebras and factorize the corresponding Shapovalov determinants which are responsible for simplicity of the highest weight modules. We apply the factorization to obtain a description of the centres of <it>Q</it>-type Lie superalgebras.