- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
Affine Fixed Point Buildings
Affine Fixed Point Buildings
- Chapter:
- (p.233) Chapter Twenty Seven Affine Fixed Point Buildings
- Source:
- Descent in Buildings (AM-190)
- Author(s):
Bernhard M¨uhlherr
Holger P. Petersson
Richard M. Weiss
- Publisher:
- Princeton University Press
This chapter shows that if Ξ is an affine building and Γ is a finite descent group of Ξ, then Γ is a descent group of Ξ∞ and (Ξ∞) is congruent to (Ξ∞). ΞΓ and Ξ can be viewed as metric spaces. The chapter first considers the assumptions that Π is an irreducible affine Coxeter diagram, Ξ is a thick building of type Ξ, Γis a finite descent group of Ξ, and Tits index �� = (Π, Θ, A). It then describes apartments that are endowed with reflection hyperplanes and reflection half-spaces before concluding with a theorem about a canonical isomorphism from the fixed point building ΞΓ to (ΞΓ).
Keywords: affine building, metric space, affine Coxeter diagram, thick building, finite descent group, Tits index, apartment, reflection hyperplane, reflection half-space, fixed point building
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- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
