Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation

Details Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation Two-dimensional affine R-buildings defined by generalized polygons with non-discrete valuation

2009-09-27

arxiv.org/abs/0909.4967v1

Mathematics

Metric Geometry

Scientific paper

In this paper we complete the proof of the "equivalence" of non-discrete R-buildings of types A~_2 and C~_2, with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in previous paper of the authors. We also complete the proof of the "equivalence" of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons). We also complement a result of the second author by proving uniqueness up to scalar multiples of the weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type A~_2 with arbitrary residues.

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