Semi-invariants of Quivers and Saturation of Littlewood-Richardson Coefficients

Abstract

Using Schofield semi-invariants, and showing a correspondence between weight spaces of semi-invariant rings for a special class of quivers, and the Littlewood-Richardson coefficients, we show that the space of Littlewood-Richardson numbers is saturated, i.e. if $c_{N \lambda, N \mu}^{N \nu} \neq 0$ then $c_{\lambda, \mu}^{\nu} \neq 0$, by showing that weights $\sigma \in \Sigma(Q, \beta)$ are saturated.