4 problems

For every $n\geqslant3$, let ${\mathcal O}(\boldsymbol{\lambda})\subset{\mathfrak{sl}}_n$ be the unique nilpotent orbit with … where ${\mathfrak b}$ is a Borel subalgebra and…

Let ${\mathcal N}\subset{\mathfrak{sl}}_n$ be the nilpotent cone, let $e\in{\mathcal N}$, and define ${\mathcal O}^{\langle k\rangle}:=SL_n\cdot e^k$ for $k\geqslant1$. Power conje…

Let $\chi$ be an $SL_n$-oper with real monodromy. Let $(\mathcal V_{\omega_1},\nabla_\chi)$ be its associated flat vector bundle, with determinant identified with the trivial flat…

Let $G=SL_n(F)$, let $x=\pi^{\mu}w\in\widetilde{W}$, and suppose that $\mu$ is dominant, meaning … for every simple root $\alpha_i$ in $\operatorname{Lie}(G)$, equivalently…