A lower bound for the dimension of a highest weight module

Abstract

For each integer t > 0 t>0 and each simple Lie algebra g \mathfrak {g} , we determine the least dimension of an irreducible highest weight representation of g \mathfrak {g} whose highest weight has width t 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.