A geometric construction of panel-regular lattices in buildings of types ~A2 and ~C2
Abstract
Using Singer polygons, we construct locally finite affine buildings of types ~A2 and ~C2 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 ~C2-buildings are necessarily exotic. To the knowledge of the author, these are the first presentations of lattices in buildings of type ~C2. Integral and rational group homology for the lattices is also calculated.
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