Abstract
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 arrangements of linear subspaces defined by sets of diagonal equalities x i =x j and invariant under the action of S n which permutes the coordinates. We provide bounds for the point when stabilization occurs and an alternative proof of the fact that stabilization happens. The latter is a special case of very general stabilization results proved independently by Gadish and by Petersen; for the pure braid space the result is part of the work of Church and Farb. For the latter space, better stabilization bounds were obtained by Hersh and Reiner.
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