4 problems

Totally positive torus conjecture. One has

Let $G_{>0}$ be the totally positive part of a reductive group $G$, let $\mathbb{T}_{>0}$ be the totally positive part of the variety $\mathbb{T}$ of maximal tori of $G$, and let ……

Conjecture 5.2. There exists a finite collection $G_1,\ldots,G_r$ of $K$-forms of $G$ such that every such $H$ is $K$-isomorphic to one of the $G_i$.

Let $E_8$ be the simply connected compact exceptional Lie group, and let $\gamma$, $\gamma'$, $\sigma$, $\sigma'$ and $\upsilon_3$ be the commuting automorphism elements used to de…