On Modular Homology in the Boolean Algebra, III

Let F be a field of characteristic p, and if Ω is an n-set let Mn be the vector space over F with basis 2Ω. We continue our investigation of modular homological Sn-representations which arise from the r-step inclusion map. This is the FSn-homomorphism ∂r: Mn → Mn which sends a k-element subset Δ Ω onto the sum of all (k − r)-element subsets of Δ. Using homological methods one can give explicit character and dimension formulae.