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- DescriptionDescent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their 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 tion of a Tits index, a combinatorial version of the tion 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 Bruhat-Tits 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 Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.
- Author BiographyBernhard Muhlherr is professor of mathematics at the University of Giessen in Germany. Holger P. Petersson is professor emeritus of mathematics at the University of Hagen in Germany. Richard M. Weiss is the William Walker Professor of Mathematics at Tufts University. He is the author of The Structure of Spherical Buildings, Quadrangular Algebras and The Structure of Affine Buildings (all Princeton) and the coauthor with Jacques Tits of Moufang Polygons.
- Author(s)Bernhard Muhlherr,Holger P. Petersson,Richard M. Weiss
- PublisherPrinceton University Press
- Date of Publication02/10/2015
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleAnnals of Mathematics Studies
- Series Part/Volume Number190
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note22 line illus. 8 tables.
- Weight514 g
- Width152 mm
- Height229 mm
- Spine23 mm
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