A Basis for the GL_n Tensor Product Algebra

Abstract

This paper focuses on the $G{L}_n$ tensor product algebra, which encapsulates the decomposition of tensor products of arbitrary finite dimensional irreducible representations of $G{L}_n$. 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 pages

References in corpus (1)

• Reciprocity Algebras and Branching for Classical Symmetric Pairs