On Lie Groups and The Theory of Complex Variables

In this note we envisage the relation existing between the Lie Groups and the Theory of Complex Variables. In particular, it is shown that the dimensions of the irreducibles representations of $SU(N)$ may be written in terms of the Eisenstein integers and an identity is built up between the imaginary parts of the dimensions of the irreducible representations of the Lie Groups $SU(3)$ and $Sp(4)$.