| Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field of positive prime characteristic. Let L(lambda) and Delta(lambda) be the simple and induced finite dimensional rational G-modules with p-singular dominant highest weight lambda. In this thesis, the concept of Weyl filtration dimension of a finite dimensional rational G-module is studied for some highest weight modules with p-singular highest weights inside the p 2-alcove when G is of type B 2. In Chapter 4, intertwining morphisms, a diagonal G-module morphism and tilting modules are used to compute the Weyl filtration dimension of L(lambda) with lambda p-singular and inside the p2 -alcove. It is shown that the Weyl filtration dimension of L(lambda) coincides with the Weyl filtration dimension of Delta(lambda) for almost all (all but one of the 6 facet types) p-singular weights inside the p2-alcove. In Chapter 5 we study some submodule structures of Weyl (and there translations), Vogan, and tilting modules with both p-regular and p-singular highest weights. Most results are for the p2-alcove only although some concepts used are alcove independent. |
