A lower bound for the dimension of a highest weight module

Abstract

Abstract. For each integer t > 0 and each simple Lie algebra g, we determine the least dimension of an irreducible highest weight representation of g whose highest weight has width t. As a consequence, we classify all irreducible modules whose dimension equals a product of two primes. This consequence, which was in fact the driving force behind our paper, answers a question of N. Katz.