Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebra $G(3)$

Abstract

We classify the blocks, compute the Verma flags of tilting and projective modules in the BGG category $\mathcal{O}$ for the exceptional Lie superalgebra $G(3)$. The projective injective modules in $\mathcal{O}$ are classified. We also compute the Jordan-Hölder multiplicities of the Verma modules in $\mathcal{O}$.

28 pages

References in corpus (2)

• \vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras
• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebras $D(2|1;\zeta )$