  Many six-dimensional $(1,0)$ SCFTs are known to fall into families labelled
by nilpotent orbits of certain simple Lie algebras. For each of the three
infinite series of such families, we show that the anomalies for the continuous
zero-form global symmetries of a theory labelled by a nilpotent orbit $O$ of
$\mathfrak{g}$ can be determined from the anomalies of the theory associated to
the trivial nilpotent orbit (the parent theory), together with the data of $O$.
In particular, knowledge of the tensor branch field theory is bypassed
completely. We show that the known anomalies, previously determined from the
geometric/atomic construction, are reproduced by analyzing the Nambu--Goldstone
modes inside of the moment map associated to the $\mathfrak{g}$ flavor symmetry
of the parent SCFT. This provides further evidence for the physics underlying
the labelling of the SCFTs by nilpotent orbits. We remark on some consequences,
such as the reinterpretation of the 6d $a$-theorem for such SCFTs in terms of
group theory.
