  We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS
circular Wilson loop of ${\cal N}=4$ super Yang Mills in terms of color
invariants, valid for any representation R of any gauge group G. This
expression allows us to discuss various exact relations among vevs in different
representations. We also display the reduction of these color invariants to
simpler ones, up to seventh order in perturbation theory, and verify that the
resulting expression is considerably simpler for the logarithm of
$\left<W\right>_R$ than for $\left<W\right>_R$ itself. We find that in the
particular case of the symmetric and antisymmetric representations of SU(N),
the logarithm of $\left<W\right>_R$ satisfies a quadratic Casimir factorization
up to seventh order, and argue that this property holds to all orders. Finally,
we derive the large N expansion of $\left<W\right>_R$ for an arbitrary, but
fixed, representation of SU(N), up to order $1/\text{N}^2$.
