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Title: Representations and cohomology of algebraic groups
Author: Anwar, Muhammad F.
ISNI:       0000 0004 2716 8989
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2011
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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.
Supervisor: Donkin, Stephen Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available