Enumerating  blueprints, and an application.

Abramson, Michael; Bennett, Curtis D.

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We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.

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We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on ${\tilde{A}}_{n}$ groups, as shown in the paper by A. Valette [same issue].

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Displaying similar documents to “Enumerating A 3 ( 2 ) blueprints, and an application.”

Displaying similar documents to “Enumerating $A_{3} (2)$ blueprints, and an application.”