The Generalized Branching Rule Of The Restricted Irreducible Representations For The Witt Superalgebra

In this dissertation, We will study the branching rule of the restricted irreducible representations for the Witt superalgebras. W(n-1) can be considered as the restricted subalgebra of W(n), and every W(n) module becomes W(n-1) module. In this article we obtains the following main results:(1) It is proved that as W(n-1) module, W(n) module K(λ) has K(μ)-filtration. In other words, there exists a submodule sequence for Kac module of W(n), such that every quotient module is isomorphic to a Kac module of W(n-1).(2) Consider the Grothendieck group of the restricted W(n)-module category and W(n-1)-module category, the generalized branching rule is determined completely.