A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2

Details A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2 A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2

2009-08-19

arxiv.org/abs/0908.2713v3

Mathematics

Group Theory

42 pages, small corrections and cleanup. Results are unchanged.

Scientific paper

Using Singer polygons, we construct locally finite affine buildings of types ~A_2 and ~C_2 which admit uniform lattices acting regularly on panels. This construction produces very explicit descriptions of these buildings as well as very short presentations of the lattices. All but one of the ~C_2-buildings are necessarily exotic. To the knowledge of the author, these are the first presentations of lattices in buildings of type ~C_2. Integral and rational group homology for the lattices is also calculated.

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