Cross-section Lattices of $\mathcal{J}$-irreducible Monoids and Orbit Structures of Weight Polytopes

Zhuo Li, You'an Cao, Zhenheng Li

Let $\lambda$ be a dominant weight of a finite dimensional simple Lie algebra and $W$ the Weyl group. The convex hull of $W\lambda$ is defined as the weight polytope of $\lambda$. We provide a new p…