Block Degeneracy for Graded Lie Superalgebras of Cartan Type

Abstract

Let $\mathbb{k}$ be an algebraically closed field of characteristic $p>0.$ In this short note, we illustrate a class of Lie superalgebras over $\mathbb{k}$ such that the category of restricted supermodules is of one block. As an application, if $p>3$ and $\mathfrak{g}$ is a graded restricted Cartan type Lie superalgebra of type W, S and H, then the category of restricted $\mathfrak{g}$ supermodules is of one block.

F.Duan, B.Shu and Y.Yao obtain a similar block degeneracy phenomenon by different methods recently