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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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Semi-ramified Quadrangles of Type E6, E7 and E8

Semi-ramified Quadrangles of Type E6, E7 and E8

(p.93) Chapter Twelve Semi-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 semi-ramified quadrangle of type E⁶, E₇ and E₈. The basic proposition is that Ξ‎ is a semi-ramified quadrangle if δ‎Λ‎ = 1 and δ‎Ψ‎ = 2 holds. The chapter first considers the theorem supposing that ℓ = 6, that δ‎Λ‎ = 1 and δ‎Ψ‎ = 2, and that the Moufang residues R0 and R1 are not both indifferent. This is followed by cases ℓ = 7 and ℓ = 8 as well as theorems concerning an anisotropic pseudo-quadratic space, a quaternion division algebra, standard involution, a proper involutory set, and isotropic and anisotropic quadratic spaces.

Keywords:   semi-ramified quadrangle, Bruhat-Tits building, residue, anisotropic pseudo-quadratic space, quaternion division algebra, standard involution, involutory set, isotropic quadratic space, anisotropic quadratic space

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