On the modular representation theory of algebraic Chevalley groups

• Main Author: Winter, Paul William
• Published: University of Warwick 1976
• Subjects: 510; QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.477730

This thesis aims to provide an introduction to the modular representation theory of algebraic Chevalley groups. Chapter 1 contains the general theory so far, most of which is due to Green [6] who sets up the modular theory in the more general context of co-algebras. In chapter 2 the decomposition matrix is discussed. In particular, its reliance on the p-restricted part is made as explicit as possible. The general results obtained are applied to the A1, A2 and B2 cases. Chapter 3 provides the simplest example of the theory, that of the group SL (2,K), K an algebraically closed field of character p ≠ 0. The structure of the Weyl module reduced modulo p is given in (3.2). This was done independently of Cline [5] In (3.3) the structure of the affine ring K[SL (2,K)] is analysed, which provides the setting for (3.5) where the injective indecomposable modules are found. Section (3.6) gives the Cartan invariants and blocks, their nature in general being conjectured at the end of' the thesis.