Let G be a semisimple simply connected linear algebraic group over an algebraically closed field k of characteristic p. In [11], 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 [11] for G = G2. In his famous paper [7], 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 [17], 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:550286 |
| Date | January 2011 |
| Creators | Anwar, Muhammad F. |
| Contributors | Donkin, Stephen |
| Publisher | University of York |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.whiterose.ac.uk/2032/ |
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