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

TL;DR

This paper classifies blocks and computes characters of tilting modules for non-integral weights in the category of modules over the exceptional Lie superalgebra G(3), establishing reduction methods to related Lie algebras.

Contribution

It provides a classification of blocks and character formulas for non-integral weight modules of G(3), connecting them to other Lie (super)algebras through reduction techniques.

Findings

Classified blocks in category O for G(3)

Computed characters for tilting modules of non-integral weights

Established reduction methods linking G(3) to other Lie algebras

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