Why should the Littlewood–Richardson Rule be true?
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We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of GL n. The core of the argument uses classical invariant theory, especially (GL n, 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. © 2011 American Mathematical Society.
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