  Let X=G/B be a complete flag variety, and L' and L" two line bundles on X.
  Consider the cup product map H^{d'}(X,L') x H^{d"}(X, L") --> H^{d}(X,L),
where L=L' x L" and d=d'+d".
  We answer two natural questions about the map above: When is it a nonzero map
of irreducible G-representations? Conversely, given generic irreducible
representations V' and V" of G, which irreducible components of V' x V" may
appear in the right hand side of the map above? We also give bounds on the
multiplicities appearing in a tensor product, and relate these considerations
to the boundary of the Littlewood-Richardson cone.
