Vol. 5, No. 3, 2011

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Toric-friendly groups

Mikhail Borovoi and Zinovy Reichstein

Vol. 5 (2011), No. 3, 361–378
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.

Keywords
toric-friendly group, linear algebraic group, semisimple group, maximal torus, rational point, elementary obstruction
Mathematical Subject Classification 2000
Primary: 20G10
Secondary: 20G15, 14G05