  This paper focuses on the $GL_n$ tensor product algebra, which encapsulates
the decomposition of tensor products of arbitrary finite dimensional
irreducible representations of $GL_n$. We will describe an explicit basis for
this algebra. This construction relates directly with the combinatorial
description of Littlewood-Richardson coefficients in terms of
Littlewood-Richardson tableaux. Philosophically, one may view this construction
as a recasting of the Littlewood-Richardson rule in the context of classical
invariant theory.
