Why should the Littlewood–Richardson Rule be true?
Why should the Littlewood–Richardson Rule be true?
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 …