Characters for Projective Modules in the BGG Category O for General Linear Lie Superalgebras

Abstract

We determine the Verma multiplicities and the characters of projective modules for atypical blocks in the BGG Category O for the general linear Lie superalgebras $\mathfrak{gl}(2|2)$ and $\mathfrak{gl}(3|1)$. We then explicitly determine the composition factor multiplcities of Verma modules in the atypicality 2 block of $\mathfrak{gl}(2|2)$.