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Generalized affine buildings

In the present thesis geometric properties of non-discrete affine buildings are studied. We cover in particular affine $Λ$-buildings, which were introduced by Curtis Bennett in 1990 and which already have proven to be useful for applications. The main results are as follow: First we prove an extension theorem for ecological isomorphisms of buildings at infinity. Further, complementing a joint project with L. Kramer and R. Weiss, we give an algebraic proof of the existence of (necessarily) non-discrete affine buildings having Suzuki-Ree buildings at infinity. Most of the effort is put in the generalization of Kostant's convexity theorem for symmetric spaces in the setting of simplicial affine and affine $Λ$-buildings. The proofs are based on connections to representation theory as well as on methods borrowed from metric geometry.