Representations of the Witt Lie Superalgebra with <Emphasis Type="Italic">p</Emphasis>-character of Height One

Let W(n) be the Witt Lie superalgebra over an algebraically closed field k of characteristic p>2. We study the representations of W(n),n≥3 with p-character of height one. We prove that the Kac module always has a unique simple quotient and all simple modules are given in this way. In fact, most Kac modules are simple. We will determine the sufficient and necessary conditions such that the Kac module is simple. Moreover, composition factors of each Kac module can be determined. It is proved that the number of composition factors in each Kac module is at most 2.