A geometrical approach to the Littlewood-Richardson rule (Q1355656)

Let \(L\) be a subgroup of \(G=\text{GL}(n,C)\) isomorphic to \(\text{GL}(m,C)\times\text{GL}(n-m,C)\), \(W\) the Weyl group of \(G\) and \(W'\) the Weyl group of \(L\). The Littlewood-Richardson rule gives the decomposition of an induced representation of an irreducible representation of \(W'\) into irreducible representations of \(W\). The author describes the right cells of \(W\) which arise in the induced representation of a right cell of \(W'\), by means of the corresponding standard tableaux. Then given a pair of standard tableaux corresponding to an irreducible representation of \(W'\), she attaches to them a set of standard tableaux corresponding to the irreducible constituents of the induced representation of \(W\). This can be regarded as a reformulation and a refinement of the Littlewood-Richardson rule.