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 $\mathfrak{osp}(3|2)$.

arXiv comment33 pages

References in corpus (6)

• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• Equivalence of blocks for the general linear Lie superalgebra
• Semi-infinite highest weight categories
• Irreducible Characters of Kac-Moody Lie superalgebras
• \vS{a}povalov elements and the Jantzen sum formula for contragredient Lie superalgebras

Cited by in corpus (1)

• Whittaker modules for classical Lie superalgebras