4 problems

Let $G$ be a connected complex reductive algebraic group with Weyl group $W$, and let $W(D_r)$ denote the Weyl group of type $D_r$. A Weyl group element $u$ is rational when the st…

Let $\Phi$ be a crystallographic root system with positive-root poset $\Phi^+$, whose order ideals are denoted by $\mathcal{J}(\Phi^+)$. An antichain is a subset of $\Phi^+$ whose…

Let $\Phi^+(A_n)$ be the positive-root poset of type $A_n$, and let the rank-alternating order ideal cardinality statistic be … for an order ideal $I$ of $\Phi^+(A_n)$. Bernstein–S…

Let $\Phi$ be a root system, let $\mathcal{M}(\Phi)$ be its diagonal coinvariant ring, and define its bigraded Hilbert series by … Let $\mathcal{I}(\Phi^+)$ denote the order ideals…