On Kac-Weisfeiler modules for general and special linear Lie superalgebras

Abstract

Let $\ggg:=\gl_{m|n}$ be a general linear Lie superalgebra over an algebraically closed field $\mathds{k}=\overline{\mathbb{F}}_p$ of characteristic $p>2$. A module of $⋙$ is said to be of Kac-Weisfeiler if its dimension coincides with the dimensional lower bound in the super Kac-Weisfeiler property presented by Wang-Zhao in \cite{WZ}. In this paper, we verify the existence of the Kac-Weisfeiler modules for $\gl_{m|n}$. We also establish the corresponding consequence for the special linear Lie superalgebras ${\mathfrak{sl}}_{m|n}$ with restrictions $p>2$ and $p\nmid (m-n)$.

15 pages

Cited by in corpus (1)

• Finite $W$-superalgebras and the dimensional lower bounds for the representations of basic Lie superalgebras