Blocks and characters of $G(3)$-modules of non-integral weights

Abstract

We classify blocks in the BGG category $\mathcal{O}$ of modules of non-integral weights for the exceptional Lie superalgebra $G(3)$. We compute the characters for tilting modules of non-integral weights in $\mathcal{O}$. Reduction methods are established to connect non-integral blocks of $G(3)$ with blocks of the special linear Lie algebra $\mathfrak{sl}(2)$, the exceptional Lie algebra $G_2$, the general linear Lie superalgebras $\mathfrak{gl}(1|1)$, $\mathfrak{gl}(2|1)$ and the ortho-symplectic Lie superalgebra $\mathfrak{osp}(3|2)$.

33 pages

References in corpus (1)

• \vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras