Toric-friendly groups

Abstract

Let $G$ be a connected linear algebraic group over a field $k$. We say that $G$ is toric-friendly if for any field extension $K∕k$ and any maximal $K$-torus $T$ in $G$ the group $G\left(K\right)$ acts transitively on $\left(G∕T\right)\left(K\right)$. Our main result is a classification of semisimple (and under certain assumptions on $k$, of connected) toric-friendly groups.