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).
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2016 ◽
Vol 2017
(1)
◽
pp. 17-30
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2018 ◽
Vol 6
(8)
◽
pp. 297
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