Depths and cores in the light of DS-functors

Abstract

The Dulfo-Serganova functors DS are tensor functors relating representations of different Lie superalgebras. In this paper we study the behaviour of various invariants, such as the defect, the dual Coxeter number, the atypicality and the cores, under the DS-functor. We introduce a notion of depth playing the role of defect for algebras and atypicality for modules. We mainly concentrate on examples of symmetrizable Kac-Moody and Q-type superalgebras.