Application of the Bruhat-Tits tree of SU₃(h)
to some ${\tilde A}_2$ groups

Donald I. Cartwright
School of Mathematics and Statistics
The University of Sydney
NSW 2006
Australia

and
Tim Steger
Istituto di Matematica e Fisica
Università di Sassari
via Vienna 2
07100 Sassari
Italy

Abstract:

Let K be a nonarchimedean local field, let L be a separable quadratic extension of K, and let h denote a nondegenerate sesquilinear form on L³. The Bruhat-Tits building associated with SU₃(h) is a tree. This is applied to the study of certain groups acting simply transitively on vertices of the building associated with SL(3,F), $F=\Q_3$ or ${\Bbb F}_3((X))$.

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