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Fixed Point Buildings
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This chapter presents the proof for the Fundamental Theorem of Descent in buildings: that if Γ is a descent group, the set of residues of a building Δ that are stabilized by a subgroup Γ of Aut(Γ) forms a thick building. It begins with the hypothesis: Let Π be an arbitrary Coxeter diagram, let S be the vertex set of Π and let (W, S) be the corresponding Coxeter system. It then defines a Γ-residue and a Γ-chamber as well as a descent group of Δ before concluding with the main result about the fixed point building of Γ.
Princeton University Press
Title: Fixed Point Buildings
Description:
This chapter presents the proof for the Fundamental Theorem of Descent in buildings: that if Γ is a descent group, the set of residues of a building Δ that are stabilized by a subgroup Γ of Aut(Γ) forms a thick building.
It begins with the hypothesis: Let Π be an arbitrary Coxeter diagram, let S be the vertex set of Π and let (W, S) be the corresponding Coxeter system.
It then defines a Γ-residue and a Γ-chamber as well as a descent group of Δ before concluding with the main result about the fixed point building of Γ.
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