Let X = G/B and let L1 and L2 be two line bundles on X. Consider the cup product map H1 (X,L1)⊗H q2 (X,L2) → H (X,L), where L = L1⊗L2 and q = q1+q2. We find necessary and sufficient conditions for this map to be a nonzero map of G–modules. We also discuss the converse question, i.e. given irreducible G–modules U and V , which irreducible components W of U⊗V may appear in the right hand side of ...