Invariants on G/U x G/U x G/U, G = SL(4,C)

Let G = SL(n,C). Let U be the standard maximal unipotent subgroup of G, i.e., the group of all upper triangular matrices with 1’s on the diagonal. The invariants of G acting by left translation on GIU x G/U x G/U are explicitly c alculated for n = 2,3 ,4. In each case, all relations among the invariantsriants are given along with a Stanley decomposition for the algebra of invariants. This theory is applied to the calculation of the decomposition of the tensor product of two finite-dimensional irreducible representations of G.