  The equivariant Kazhdan-Lusztig polynomial of a braid matroid may be
interpreted as the intersection cohomology of a certain partial
compactification of the configuration space of n distinct labeled points in the
plane, regarded as a graded representation of the symmetric group. We show
that, in fixed cohomological degree, this sequence of representations of
symmetric groups naturally admits the structure of an FS-module, and that the
dual FS^op-module is finitely generated. Using the work of Sam and Snowden, we
give an asymptotic formula for the dimensions of these representations and
obtain restrictions on which irreducible representations can appear in their
decomposition.
