  Let $G$ be a connected simply connected noncompact classical simple Lie group
of Hermitian type. Then $G$ has unitary highest weight representations. The
proof of the classification of unitary highest weight representations of $G$
given by Enright, Howe and Wallach is based on the Dirac inequality of
Parthasarathy, Jantzen's formula and Howe's theory of dual pairs where one
group in the pair is compact. In this paper we focus on the Dirac inequality
which can be used to prove the classification in a more direct way.
