Stable decompositions for some symmetric group characters arising in braid group cohomology

We prove that certain permutation characters for the symmetric group Σn decompose in a manner that is independent of n for large n. This result is a key ingredient in the recent work of T. Church and B. Farb, who obtain a “representation stability” theorem for the character of Σn acting on the cohomology Hp(Pn,C) of the pure braid group Pn.