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

Let $F$ be an algebraically closed field of prime characteristic,and $W(m,n,textbf{1})$ be the simple restricted Lie superalgebra ofWitt type over $F$, which is the Lie superalgebra ofsuperderivations of the superalgebra $fraka(m;textbf{1})otimeswedge(n)$, where $fraka(m;textbf{1})$ is the truncated polynomialalgebra with $m$ indeterminants and $wedge(n)$ is the Grassmannalgebra with $n$ indeterminants. In this paper, the authordetermines the character formulas for a class of simple restrictedmodules of $W(m,n,textbf{1})$ with atypical weights of type I.