2 problems

Let $\mathfrak g$ be a finite-dimensional reductive Lie algebra of rank $l$ over an algebraically closed field of characteristic zero. For $x\in\mathfrak g$, let $\mathfrak g_x$ be…

Let ${\mathfrak g}$ be a reductive Lie algebra, and let ${\mathfrak g}^x$ denote the centralizer of $x\in{\mathfrak g}^*$. Write ${\rm ind}\,{\mathfrak h}$ for the index of a Lie a…