# Reduction rules for Littlewood-Richardson coefficients

```@inproceedings{Roth2010ReductionRF,
title={Reduction rules for Littlewood-Richardson coefficients},
author={Mike Roth},
year={2010}
}```
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 of smaller rank. In the type A case this result has already been proved by Derksen and Weyman using quivers, and by… CONTINUE READING

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