Journal of the
Korean Mathematical Society JKMS

The spherical buildings associated with absolutely simple algebraic groups of relative rank~$2$ are all Moufang polygons. Tits polygons are a more general class of geometric structures that includes Moufang polygons as a special case. Dagger-sharp Tits $n$-gons exist only for $n=3$, $4$, $6$ and~$8$. Moufang octagons were classified by Tits. We show here that there are no dagger-sharp Tits octagons that are not Moufang. As part of the proof it is shown that the same conclusion holds for a certain class of dagger-sharp Tits quadrangles.

Keywords: Building, Moufang polygon, Tits polygon, exceptional group

MSC numbers: 20E42, 51E12, 51E24

Supported by: This work was partially supported DFG Grant MU 1281/7-1 and by Simons Foundation Collaboration Grant 516364