Specht modules and incidence matrices

Abstract. We give representation theoretic interpretation for the terms in Wilson's rank formula (1.2) for the inclusion matrices of complete uniform families. We exhibit a dual Specht filtration of a suitable adjoint Radon map whose factors contribute the terms in the rank formula. From a representation theoretic point of view we give descriptions for the (complete) kernel and image of these maps in the case of partitions with at most two parts. The primary tools are the Specht filtration given by James in [10], and, in the dual setting, the work on polynomial functions by Friedl and Rónyai [6].