A Basis for the GL_n Tensor Product Algebra

Details A Basis for the GL_n Tensor Product Algebra A Basis for the GL_n Tensor Product Algebra

2004-07-27

arxiv.org/abs/math/0407468v2

Advances in Mathematics; Vol 196/2 pp 531-564 (2005)

Mathematics

Representation Theory

34 pages

Scientific paper

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.

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