2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100827This 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.34 pagesRepresentation Theorytext