11 problems

Let $\mathfrak{g}$ be a semisimple Lie algebra over an algebraically closed field of characteristic $0$, and let $x\in\mathfrak{g}$. By $C_{\mathfrak{g}}(x)$ denote the centralizer…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{E_7(a_5)}$ be the nilpotent orbit of Bala–Carter type $E_7(a_5)$ in $E_7$. Associated-variety…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{F_4(a_3)}$ be the nilpotent orbit of Bala–Carter type $F_4(a_3)$ in $F_4$. Level $-6$ $F_4$ co…

Let $X_V$ denote the associated variety of a vertex algebra $V$, and let $\mathbb{O}_{E_6(a_1)}$ be the nilpotent orbit of Bala–Carter type $E_6(a_1)$ in $E_6$. Associated-variety…

Let $N$ be a positive integer, and let $Obs_N(0)$ denote the local operators of the theory on a stack of $N$ fivebranes wrapping $C^3$ in $R\times C^5$. Let $\mathcal G_N$ be the l…

Let $E_6$, $E_7$, $E_8$, and $F_4$ denote the corresponding simple exceptional Lie algebras, and let the labels such as $2A_2$, $A_2+3A_1$, $E_6$, and $\widetilde A_2$ denote nilpo…

Let $p=2$, and let $\mathfrak{g}$ be of type $E_7$ with maximal subalgebra $M_7$ and $M_7$-invariant subspace $L'_{-1}$ as in Theorem none7p2. For the Weisfeiler filtration…

Let $p=2$, and let $\mathfrak{g}$ be of type $E_8$ with maximal subalgebra $M_8$ and $M_8$-invariant subspace $L'_{-1}$ as in Theorem none8p2. For the Weisfeiler filtration…

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over a field of characteristic $5$. Let $M$ be a maximal subalgebra of Cartan or M…

Let $G$ be an algebraic group of type $E_8$ with Lie algebra $\mathfrak{g}=\operatorname{Lie}(G)$ over an algebraically closed field of characteristic $5$. Let $M$ be a maximal sub…

Let $G$ be one of the exceptional Lie groups, let $(V,\pi)$ be respectively the $7$-, $26$-, $27$-, $56$-, or $248$-dimensional representation for $G_2$, $F_4$, $E_6$, $E_7$, or…