The Structure of Affine Buildings

by Weiss, Richard M.

• ISBN13: 9780691138817
• ISBN10: 0691138818
• Format: Paperback
• Copyright: 2008-09-08
• Publisher: Princeton Univ Pr

Summary

InThe Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss'sThe Structure of Spherical Buildings,The Structure of Affine Buildingsis organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss'sMoufang Polygons.

Table of Contents

Preface	p. vii
Affine Coxeter Diagrams	p. 1
Root Systems	p. 13
Root Data with Valuation	p. 25
Sectors	p. 39
Faces	p. 45
Gems	p. 53
Affine Buildings	p. 59
The Building at Infinity	p. 67
Trees with Valuation	p. 77
Wall Trees	p. 89
Panel Trees	p. 101
Tree-Preserving Isomorphisms	p. 107
The Moufang Property at Infinity	p. 119
Existence	p. 131
Partial Valuations	p. 147
Bruhat-Tits Theory	p. 159
Completions	p. 167
Automorphisms and Residues	p. 175
Quadrangles of Quadratic Form Type	p. 189
Quadrangles of Indifferent Type	p. 205
Quadrangles of Type E[subscript 6], E[subscript 7] and E[subscript 8]	p. 209
Quadrangles of Type F[subscript 4]	p. 221
Quadrangles of Involutory Type	p. 229
Pseudo-Quadratic Quadrangles	p. 239
Hexagons	p. 261
Assorted Conclusions	p. 275
Summary of the Classification	p. 289
Locally Finite Bruhat-Tits Buildings	p. 297
Appendix A	p. 321
Appendix B	p. 343
Bibliography	p. 361
Index	p. 365
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