Representations of Algebraic Groups

Abstract

Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)