Minuscule weights in the root lattice are zero
= Minuscule weights in the root lattice are zero
By <dominant root-lattice highest weights have zero weight>, a <minuscule weight> in the <root lattice> has zero in its <Weyl group> orbit. Since every element of the <Weyl group> is invertible, the highest weight must itself be zero. Thus equality of the <weight lattice> and <root lattice> rules out every nontrivial <minuscule representation> without requiring a classification of <root systems>.