3 problems

Let $\mathfrak{g}$ be the Lie algebra of type $B_n$, let $1\leq i\leq n$, and let $m$ be a nonnegative integer. Let $S(\mathbf D,m\omega_i)$ be the lattice points of the polytope…

Let $\mathfrak{g}$ be a Lie algebra of type $B_n$, let $\lambda=m\omega_i$ be a rectangular dominant integral weight, and let $P(\lambda)$ and $S(\lambda)$ be the polytope and its…

Demazure–PBW conjecture. In the setting of the cited Demazure-module description, one has