Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over Z(p) for representations with p-small weights

Let G be a connected reductive linear algebraic group defined and split over Z, let T be a maximal torus, W the Weyl group, R the root system, R the set of coroots, R a set of positive roots, and ρ the half-sum of the elements of R. Let X = X(T ) be the character group of T and let X be the set of those λ ∈ X such that 〈λ, α〉 ≥ 0 for all α ∈ R. For any λ ∈ X, let VZ(λ) be the Weyl module for G over Z with highest weight λ (see 1.3) and, for any commutative ring A, let VA(λ) = VZ(λ)⊗Z A. Let p be a prime integer and let