4 problems

Let $\lambda\in P^+$, let $\boldsymbol\omega\in\mathcal P_q^+$ be preminimal of order $2$, and let $L(\boldsymbol\omega)$ be the graded limit of $V_q(\boldsymbol\omega)$. Let…

Let $\boldsymbol\omega\in\mathcal P_q^+$ be preminimal of order $2$, let $k\in\partial I$ be the node such that $\boldsymbol\omega$ is not $k$-minimal, and let $i_*$ be the opposit…

Let $\mathfrak g$ be a simple Lie algebra of type $D$ or $E$, let $\mathcal P_q^+$ denote the set of dominant Drinfeld polynomials, and let $\boldsymbol\omega\in\mathcal P_q^+$ be…

Let $\mathfrak g$ be a finite-dimensional simple Lie algebra of type $D$ or $E$, and let $\lambda$ be a dominant integral weight whose support bounds a subdiagram of type $D_4$. Co…