Representations Of The Modular Witt Superalgebra W(2)

Let K be an algebraically closed field of characteristic p>0, W(2) be the superderiva-tions of the grassmann algebra of rank2over K. The representations of W(2) has two cases by isomorphism:restricted and non-restricted. In this dissertation, the maximal submod-ules are finded over the two cases by induced module. So the irreducible modules and their dimension are finded completely. In detail, this article contains the following main results:(1)When χ=0, there are two cases for atypical λ, λ=a∈1+∈2and λ=a∈2the basises of maximal submodule for Kχ(λ) are given for each case;(2)When χ≠0, the GL(2) orbits of gl(2) under adjoint action are considered for χ respectively. When Kχ(λ) is simple is studied. Furthermore, the necessary and sufficient conditoin is given when Kχ(λ) is not simple.