If a group Γ acts simply transitively on the vertices of an affine building Δ with connected diagram, then Δ must be of type Ã_{n-1) for some n ≥ 2, and Γ must have a presentation of a simple type. The case n=2, when Δ is a tree, has been studied in detail. We consider the case n=3, motivated particularly by the case when Δ is the building of G=PGL(3,K), K a local field, and when Γ ≤ G. We exibit such a group Γ when K=F_q((X)), q any prime power. Our study leads to combinatorial objects which we call triangle presentations. These triangle presentations give rise to some new buildings of type Ã2

Groups acting simply transitively on the vertices of a building of type Ã2 , I / Anna Maria Mantero; Donald Cartwright; Tim Steger; Anna Zappa. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 47(1993), pp. 143-166.

Groups acting simply transitively on the vertices of a building of type Ã2 , I

MANTERO, ANNA MARIA;ZAPPA, ANNA
1993

Abstract

If a group Γ acts simply transitively on the vertices of an affine building Δ with connected diagram, then Δ must be of type Ã_{n-1) for some n ≥ 2, and Γ must have a presentation of a simple type. The case n=2, when Δ is a tree, has been studied in detail. We consider the case n=3, motivated particularly by the case when Δ is the building of G=PGL(3,K), K a local field, and when Γ ≤ G. We exibit such a group Γ when K=F_q((X)), q any prime power. Our study leads to combinatorial objects which we call triangle presentations. These triangle presentations give rise to some new buildings of type Ã2
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/387292
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