Anwar, Muhammad F (2011) Representations and Cohomology of Algebraic Groups. PhD thesis, University of York.
Available under License Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales.
Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In , Donkin gave a recursive description for the characters of cohomology of line bundles on the flag variety G/B with G = SL3. In chapter 2 of this thesis we try to give a non recursive description for these characters. In chapter 3, we give the first step of a version of formulae in  for G = G2. In his famous paper , Demazure introduced certain indecomposable modules and used them to give a short proof of the Borel-Weil-Bott theorem (characteristic zero). In chapter 5 we give the cohomology of these modules. In a recent paper , Doty introduces the notion of r−minuscule weight and exhibits a tensor product factorization of a corresponding tilting module under the assumption p >= 2h − 2, where h is the Coxeter number. In chapter 4, we remove the restriction on p and consider some variations involving the more general notion of (p,r)−minuscule weights.
|Item Type:||Thesis (PhD)|
|Academic Units:||The University of York > Mathematics (York)|
|Depositing User:||Mr. Muhammad Fazeel Anwar|
|Date Deposited:||17 Jan 2012 15:19|
|Last Modified:||08 Aug 2013 08:47|