A Basis for the GL_n Tensor Product Algebra

Howe, Roger E.; Tan, Eng Chye; Willenbring, Jeb F.

A Basis for the GL_n Tensor Product Algebra

Authors

Howe, Roger E.

Tan, Eng Chye

Willenbring, Jeb F.

Description

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.
34 pages