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Affine Fixed Point Buildings
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This chapter shows that if Ξ is an affine building and Γ is a finite descent group of Ξ, then Γ is a descent group of Ξ∞ and (Ξ∞) is congruent to (Ξ∞). ΞΓ and Ξ can be viewed as metric spaces. The chapter first considers the assumptions that Π is an irreducible affine Coxeter diagram, Ξ is a thick building of type Ξ, Γis a finite descent group of Ξ, and Tits index �� = (Π, Θ, A). It then describes apartments that are endowed with reflection hyperplanes and reflection half-spaces before concluding with a theorem about a canonical isomorphism from the fixed point building ΞΓ to (ΞΓ).
Princeton University Press
Title: Affine Fixed Point Buildings
Description:
This chapter shows that if Ξ is an affine building and Γ is a finite descent group of Ξ, then Γ is a descent group of Ξ∞ and (Ξ∞) is congruent to (Ξ∞).
ΞΓ and Ξ can be viewed as metric spaces.
The chapter first considers the assumptions that Π is an irreducible affine Coxeter diagram, Ξ is a thick building of type Ξ, Γis a finite descent group of Ξ, and Tits index �� = (Π, Θ, A).
It then describes apartments that are endowed with reflection hyperplanes and reflection half-spaces before concluding with a theorem about a canonical isomorphism from the fixed point building ΞΓ to (ΞΓ).
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