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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

Chapter:
(p.91) Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8
Source:
Descent in Buildings (AM-190)
Author(s):

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691166902.003.0011

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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