On representations of restricted Lie superalgebras

Abstract

Simple modules for restricted Lie superalgebras are studied. The indecom-posability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type A(n|0), the baby Verma modules Z χ (λ) are proved to be simple for any regular nilpotent p-character χ and typical weight λ. Moreover, we obtain the dimension formulas for projective covers of simple modules with p-characters of standard Levi form.