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THE EXCEPTIONAL TITS QUADRANGLES
Transformation Groups ( IF 0.784 ) Pub Date : 2020-05-22 , DOI: 10.1007/s00031-020-09573-5
BERNHARD MÜHLHERR, RICHARD M. WEISS

A Tits polygon is a bipartite graph in which the neighborhood of each vertex is endowed with an “opposition relation” satisfying certain axioms. Moufang polygons are precisely the Tits polygons in which these opposition relations are all trivial. Every Tits polygon has a distinguished set of circuits. A Tits quadrangle is a Tits polygon in which these circuits all have length 8. There is a standard construction that produces a Tits polygon from certain pairs (∆, T), where ∆ is an irreducible spherical building and T is a Tits index of relative rank 2. We call a Tits quadrangle exceptional if it arises from such a pair (∆, T) for ∆ the spherical building associated to the group of rational points of an exceptional algebraic group. In this paper, we characterize the exceptional Tits quadrangles as extensions of orthogonal Tits quadrangles in a suitable sense.
更新日期:2020-05-22

 

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