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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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Indices for the Exceptional Bruhat-Tits Buildings

Indices for the Exceptional Bruhat-Tits Buildings

(p.309) Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter considers the affine Tits indices for exceptional Bruhat-Tits buildings. It begins with a few small observations and some notations dealing with the relative type of the affine Tits indices, the canonical correspondence between the circles in a Tits index and the vertices of its relative Coxeter diagram, and Moufang sets. It then presents a proposition about an involutory set, a quaternion division algebra, a root group sequence, and standard involution. It also describes Θ‎-orbits in S which are disjoint from A and which correspond to the vertices of the Coxeter diagram of Ξ‎ and hence to the types of the panels of Ξ‎. Finally, it shows how it is possible in many cases to determine properties of the Moufang set and the Tits index for all exceptional Bruhat-Tits buildings of type other than Latin Capital Letter G with Tilde₂.

Keywords:   involutory set, Tits index, Coxeter diagram, Moufang set, quaternion division algebra, root group sequence, standard involution, Bruhat-Tits building

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