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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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Quadrangles of Type E6, E7 and E8: Summary

Quadrangles of Type E6, E7 and E8: Summary

(p.109) Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter summarizes the different cases about Moufang quadrangles of type E⁶, E₇ and E₈. The first case is that the building at infinity of the Bruhat-Tits building Ξ‎ is an unramified quadrangle; the second, a semi-ramified quadrangle; and the third, a ramified quadrangle. The chapter considers a theorem that takes into account two root group sequences, both of which are either indifferent or the various dimensions, types, etc., are as indicated in exactly one of twenty-three cases. It also presents a number of propositions relating to a quaternion division algebra and a quadratic space of type Eℓ for ℓ = 6, 7 or 8. Finally, it emphasizes the fact that the quadrangles of type F₄ could have been overlooked in the classification of Moufang polygons.

Keywords:   unramified quadrangle, Moufang quadrangle, Bruhat-Tits building, semi-ramified quadrangle, ramified quadrangle, root group sequence, quaternion division algebra, quadratic space, Moufang polygon

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