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The equivariant Kazhdan-Lusztig polynomial of a braid matroid may beinterpreted as the intersection cohomology of a certain partialcompactification of the configuration space of n distinct labeled points in theplane, regarded as a graded representation of the symmetric group. We showthat, in fixed cohomological degree, this sequence of representations ofsymmetric groups naturally admits the structure of an FS-module, and that thedual FS^op-module is finitely generated. Using the work of Sam and Snowden, wegive an asymptotic formula for the dimensions of these representations andobtain restrictions on which irreducible representations can appear in theirdecomposition.

Configuration spaces, $\operatorname{FS^{op}}$-modules, and Kazhdan-Lusztig polynomials of braid matroids