Irreducible Representations Of Jacobson-Witt Algebra

In this paper, we mainly used polynomial representations decomposition theory of general linear group to concern irreducible representations of Jacobson-Witt algebra. Under the graded construction of Jacobson-Witt algebra , we have proved that it's graded subspace of degree less than p - n can be decomposed into two irreducible GL(n) modules . we mainly researched dimensions and classes of irreducible modules of W(3) with p-character x and rank(x) equal to 1.