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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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Orthogonal Buildings

Orthogonal Buildings

(p.303) Chapter Thirty Five Orthogonal Buildings
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter presents a few results about certain forms of orthogonal buildings. It begins with notations stating that V is a K-vector space of positive dimension, (K, V, q) is a quadratic space of positive dimension, (K, V, q) is a regular quadratic space of positive Witt index, S is the vertex set of the Coxeter diagram, (K, V, q) is a hyperbolic quadratic space of dimension 2n for some n greater than or equal to 3, S is the vertex set of the Coxeter diagram for some n greater than or equal to 3, and Dn.l,script small l is the Tits index of absolute type Dn for n greater than or equal to 3. The chapter also considers propositions dealing with regular quadratic spaces and hyperbolic quadratic spaces.

Keywords:   orthogonal building, quadratic space, Witt index, vertex, Coxeter diagram, hyperbolic quadratic space, Tits index

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