  The Coulomb and Higgs branches of certain 3d N=4 gauge theories can be
understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa
suggests that this is the simplest possible case, thus giving this class a
special role. In this note we use branes to reproduce the mathematical work by
Kraft and Procesi. It studies the classification of all nilpotent orbits for
classical groups and it characterizes an inclusion relation via minimal
singularities. We show how these minimal singularities arise naturally in the
Type IIB superstring embedding of the 3d A-type theories. The Higgs mechanism
can be used to remove the minimal singularity, corresponding to a transition in
the brane configuration that induces a new effective 3d theory. This reproduces
the Kraft-Procesi results, endowing the family of gauge theories with a new
underlying structure. We provide an efficient procedure for computing such
brane transitions.
