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Descent in Buildings (AM-190)$
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Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Print publication date: 2015

Print ISBN-13: 9780691166902

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691166902.001.0001

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Ramified Quadrangles of Type E6, E7 and E8

Ramified Quadrangles of Type E6, E7 and E8

(p.101) Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter deals with the case that the building at infinity of the Bruhat-Tits building Ξ‎ is a Moufang ramified quadrangle of type E⁶, E₇ and E₈. The basic proposition is that Ξ‎ is a ramified quadrangle if δ‎Λ‎ = δ‎Ψ‎ = 1 holds. The chapter proves the theorem that if δ‎Ψ‎ = 1 and the Moufang residues R₀ and R₁ are not both indifferent, there exists an involutory set. It also discusses the cases ℓ = 6, ℓ = 7, and ℓ = 8, in which D is a quaternion division algebra.

Keywords:   ramified quadrangle, Bruhat-Tits building, residue, involutory set, quaternion division algebra

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