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Descent in Buildings (AM-190)

Online ISBN:
9781400874019
Print ISBN:
9780691166902
Publisher:
Princeton University Press
Book

Descent in Buildings (AM-190)

Bernhard Mühlherr,
Bernhard Mühlherr
Universitat Giessen
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Holger P. Petersson,
Holger P. Petersson
FernUniversität in Hagen
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Richard M. Weiss
Richard M. Weiss
Tufts University
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Published:
15 September 2015
Online ISBN:
9781400874019
Print ISBN:
9780691166902
Publisher:
Princeton University Press

Abstract

This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or “form” of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a “residually pseudo-split” building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with The Structure of Spherical Buildings and The Structure of Affine Buildings.

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