Reduction Rules for Littlewood-richardson Coefficients
نویسنده
چکیده
Let G be a semisimple algebraic group over an algebraically-closed field of characteristic zero. In this note we show that every regular face of the Littlewood-Richardson cone of G gives rise to a reduction rule: a rule which, given a problem “on that face” of computing the multiplicity of an irreducible component in a tensor product, reduces it to a similar problem on a group G of smaller rank. In the type A case this result has already been proved by Derksen and Weyman using quivers, and by King, Tollu, and Toumazet using puzzles. The proof here is geometric and type-independent.
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