  Garsia and Procesi, in their study of Springer's representation, proved that
the cohomology ring of a Springer fiber is isomorphic to the associated graded
ring of the coordinate ring of the $S_n$ orbit of a single point in
$\mathbb{C}^n$. This construction was an essential tool in their analysis of
the Springer representation, and variations of it have reappeared recently in
several other combinatorial and geometric contexts under the name orbit
harmonics. In this article, we analyze the orbit harmonics of a union of two
$S_n$ orbits. We prove that when the coordinate sums of the two orbits are
different, the corresponding graded $S_n$ representation is a direct sum of two
Springer representations, one of which is shifted in degree by 1.
