  The strongly interacting 4d N=2 SCFT's of type $(A_n,A_m)$ are the simplest
examples of models in the $(G,G^\prime)$ class introduced by Cecotti, Neitzke,
and Vafa in arXiv:1006.3435. These systems have a known 3d N=4 mirror only if
$h(A_n)$ divides $h(A_m)$, where $h$ is the Coxeter number. By 4d/2d
correspondence, we show that in this case these systems have a nontrivial
global flavor symmetry group and, therefore, a non-trivial Higgs branch. As an
application of the methods of arXiv:1309.2657, we then compute the refined
Hilbert series of the Coulomb branch of the 3d mirror for the simplest models
in the series. This equals the refined Hilbert series of the Higgs branch of
the $(A_n,A_m)$ SCFT, providing interesting information about the Higgs branch
of these non-lagrangian theories.
