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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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Unramified Quadrangles of Type E6, E7 and E8

Unramified Quadrangles of Type E6, E7 and E8

(p.91) Chapter Eleven Unramified 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 quadrangle of type E⁶, E₇, and E₈. It begins with a hypothesis that takes into account a quadratic space of type Eℓ for ℓ = 6, 7 or 8, K which is complete with respect to a discrete valuation, the two residues of Ξ‎, and the two root group sequences of a Moufang polygon. It then considers the case that Ξ‎ is an unramified quadrangle if the proposition δ‎Ψ‎ = 2 holds. It also explains two other propositions: Ξ‎ is a semi-ramified quadrangle if δ‎Λ‎ = 1 and δ‎Ψ‎ = 2 holds, and a ramified quadrangle if δ‎Λ‎ = δ‎Ψ‎ = 1 holds.

Keywords:   quadratic space, Bruhat-Tits building, Moufang quadrangle, discrete valuation, residue, root group sequence, Moufang polygon, unramified quadrangle, semi-ramified quadrangle, ramified quadrangle

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