Generalized affine buildings

Abstract

In the present thesis geometric properties of non-discrete affine buildings are studied. We cover in particular affine $\Lambda$-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 $\Lambda$-buildings. The proofs are based on connections to representation theory as well as on methods borrowed from metric geometry.

doctoral thesis, Muenster, November 2008, 99 pages, 17 figures

References in corpus (4)

• Affine buildings for dihedral groups
• Alcove walks, buildings, symmetric functions and representations
• Kostant Convexity for affine buildings
• Non-discrete Euclidean Buildings for the Ree and Suzuki groups

Cited by in corpus (4)

• Axioms of affine buildings
• A structure theorem for euclidean buildings
• Rigidity at infinity of trees and Euclidean buildings
• On epimorphisms of spherical Moufang buildings