Journal of Algebra | 2021
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 $\\mathfrak{osp}(3|2)$.