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Why should the Littlewood-Richardson Rule be true?

Authors: Roger Howe and Soo Teck Lee
Journal: Bull. Amer. Math. Soc. 49 (2012), 187-236
MSC (2000): Primary 20G05; Secondary 05E15
Posted: October 20, 2011
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Abstract: We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of $\textrm {GL}_n$ . The core of the argument uses classical invariant theory, especially $(\textrm {GL}_n, \textrm {GL}_m)$ -duality. Both of the main conditions (semistandard condition, lattice permutation/Yamanouchi word condition) placed on the tableaux used to define Littlewood-Richardson coefficients have natural interpretations in the argument.

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