The Exceptional Tits Quadrangles Revisited

Abstract

Tits polygons are generalizations of Moufang polygons in which the neighborhood of each vertex is endowed with an “opposition relation.” There is a standard construction that produces a Tits polygon from an arbitrary irreducible spherical building of rank at least 3 when paired with a suitable Tits index. In this note, we complete the proof of a characterization of the Tits quadrangles that arise in this way from the spherical building associated to an exceptional algebraic group.