Why should the Littlewood–Richardson Rule be true?

We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of GLₙ. The core of the argument uses classical invariant theory, especially (GLₙ, GLₘ)-duality. Both of the main conditions (semistandard condition, lattice permutation/Yamanouchi word condition) placed on the tableaux used to define Littlewood-Richardson coefficients have natural interpretations in the argument.