  Supersolvable hyperplane arrangements and matroids are known to give rise to
certain Koszul algebras, namely their Orlik-Solomon algebras and graded
Varchenko-Gel'fand algebras. We explore how this interacts with group actions,
particularly for the braid arrangement and the action of the symmetric group,
where the Hilbert functions of the algebras and their Koszul duals are given by
Stirling numbers of the first and second kinds, respectively. The corresponding
symmetric group representations exhibit branching rules that interpret Stirling
number recurrences, which are shown to apply to all supersolvable arrangements.
They also enjoy representation stability properties that follow from Koszul
duality.
