# WEYL filtration dimension and submodule structures for B2

Abstract (Summary)

Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field of positive prime characteristic. Let L([lambda]) and [upside-down triangle]([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 p2-alcove when G is of type B[subscript]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 p[superscript]2-alcove. It is shown that the Weyl filtration
dimension of L([lambda]) coincides with the Weyl filtration dimension of [upside-down triangle]([lambda]) for almost all (all but one of the 6 facet types) p-singular weights inside the p[superscript]2-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 p[superscript]2 -alcove only
although some concepts used are alcove independent.
Bibliographical Information:

Advisor:

School:Kansas State University

School Location:USA - Kansas

Source Type:Master's Thesis

Keywords:mathematics algebra representation theory algebraic groups 0405

ISBN:

Date of Publication:01/01/2009