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Representations and Cohomology of Algebraic Groups

Anwar, Muhammad F (2011) Representations and Cohomology of Algebraic Groups. PhD thesis, University of York.

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Abstract

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.

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
URI: http://etheses.whiterose.ac.uk/id/eprint/2032

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