  We study representation stability in the sense of Church and Farb of
sequences of cohomology groups of complements of arrangements of linear
subspaces in real and complex space as $S_n$-modules. We consider arrangement
of linear subspaces defined by sets of diagonal equalities $x_i = x_j$ and
invariant under the action of $S_n$ permuting the coordinates. We provide
bounds on the point when stabilization occurs and an alternative proof for the
fact that stabilization happens. The latter is a special case of a very general
stabilization result of Gadish and for the pure braid space the result is part
of the work of Church and Farb. For this space better stabilization bounds were
obtained by Hersh and Reiner.
