Two-Dimensional Ane R-Buildings De-ned by Generalized Polygons with Non-Discrete Valuation

Hendrik van Maldeghem, Koen Struyve
2011 Pure and Applied Mathematics Quarterly  
In this paper we complete the proof of the 'equivalence' of nondiscrete R-buildings of types A 2 and C 2 , with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in [7] . 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), begun in [14] . We also complement the main result of [13] by proving uniqueness up to scalar multiples of
more » ... he 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.
doi:10.4310/pamq.2011.v7.n3.a11 fatcat:flll3t4iizc4tj5ei6twsfvesa