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A Basis for the GL_n Tensor Product Algebra

Roger E. Howe·Eng Chye Tan·Jeb F. Willenbring
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Abstract

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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BibTeXRIS

Roger E. Howe, Eng Chye Tan, Jeb F. Willenbring. 2005-11-06. A Basis for the GL_n Tensor Product Algebra. https://arxiv.org/abs/math/0407468

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