Character Formulas for a Class of Simple Restricted Modules over the Simple Lie Superalgebras of Witt Type

Abstract

Let F be an algebraically closed field of prime characteristic, and W(m, n, 1) be the simple restricted Lie superalgebra of Witt type over F, which is the Lie superalgebra of superderivations of the superalgebra $$\mathfrak{A}(m;1)\otimes\wedge(n)$$, where $$\mathfrak{A}(m;1)$$ is the truncated polynomial algebra with m indeterminants and ∧(n) is the Grassmann algebra with n indeterminants. In this paper, the author determines the character formulas for a class of simple restricted modules of W(m, n, 1) with atypical weights of type I.