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Application of the Bruhat-Tits tree of SU3(h) to some Ã2 groups

Part of: Finite geometry and special incidence structures Forms and linear algebraic groups Lie groups

Published online by Cambridge University Press:  09 April 2009

Donald I. Cartwright  and
Tim Steger
Donald I. Cartwright
Affiliation:
School of Mathematics and Statistics The University of SydneyNSW 2006, Australia
Tim Steger
Affiliation:
Istituto di Matematica e Fisica Università di Sassarivia Vienna 207100 Sassari, Italy
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Abstract

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Let K be a nonarchimedean local field, let L be a separable quadratic extension of K, and let h denote a nondegenerate sesquilinear formk 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 = Q3 or F3((X)).

Keywords

Buildingstreeslocal fields.

MSC classification

Secondary: 51E24: Buildings and the geometry of diagrams 22E40: Discrete subgroups of Lie groups 11E95: $p$-adic theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 3 , June 1998 , pp. 329 - 344
Copyright
Copyright © Australian Mathematical Society 1998

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