WEYL filtration dimension and submodule structures for B2
dc.contributor.author | Beswick, Matthew | |
dc.date.accessioned | 2009-03-24T14:07:13Z | |
dc.date.available | 2009-03-24T14:07:13Z | |
dc.date.graduationmonth | May | en |
dc.date.issued | 2009-03-24T14:07:13Z | |
dc.date.published | 2009 | en |
dc.description.abstract | 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. | |
dc.description.advisor | Zongzhu Lin | en |
dc.description.degree | Doctor of Philosophy | en |
dc.description.department | Department of Mathematics | en |
dc.description.level | Doctoral | en |
dc.identifier.uri | http://hdl.handle.net/2097/1303 | |
dc.language.iso | en_US | en |
dc.publisher | Kansas State University | en |
dc.subject | Mathematics | en |
dc.subject | Algebra | en |
dc.subject | Representation theory | en |
dc.subject | Algebraic groups | en |
dc.subject.umi | Mathematics (0405) | en |
dc.title | WEYL filtration dimension and submodule structures for B2 | en |
dc.type | Dissertation | en |