  We investigate an effective flavor-symmetric Yang-Mills-Higgs model with
$N^2-1$ adjoint scalar fields. We find a set of BPS equations that provide
vortex solutions and calculate their energies for arbitrary representations. We
show that, for a given N-ality $k$, the energy of the corresponding
antisymmetric representation is the lowest. This completes the proof that this
model is able to reproduce a Casimir law for the string tension at asymptotic
distances.
