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

Let g:= gl (m) | (n) be a general linear Lie superalgebra over an algebraically closed field k:= of characteristic p > 2. A module of g is said to be of Kac-Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac-Weisfeiler property presented by Wang-Zhao in [9]. 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 superalgebra sl (m) | (n) with the restrictions that p > 2 and p acurrency sign (m - n).