A lower bound for the dimension of a highest weight module
  For each integer $t>0$ and each complex simple Lie algebra $\mathfrak{g}$, we determine the least dimension of an irreducible highest weight representation of $\mathfrak{g}$ whose highest weight has height $t$. As a corollary, we classify all irreducible modules whose dimension equals a product of two primes. 
Daniel Goldstein, Robert Guralnick, and Richard Stong
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