Introduction

Abstract

By a classification of mathematics due to N. Bourbaki, various parts of mathematics may be divided, according to their approach, into two large groups. The first group consists of subjects such as set theory, algebra or general topology, where the emphasis is put on the analysis of the enormously rich structures arising from a very short list of axioms. The second group, whose typical representative is algebraic geometry, consists of those subjects where the emphasis is on the synthesis arising from the interaction of different sorts of structures. Reprsentation theory undoubtedly belongs to the second group, and we have tried in this work to show how various “difficult” representation-theoretic results often follow quite easily when placed in the appropriate geometric or algebraic context.