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Indices for the Exceptional Bruhat-Tits Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0036
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter considers the affine Tits indices for exceptional Bruhat-Tits buildings. It begins with a few small observations and some notations dealing with the relative type of the affine Tits ... More


Forms of Residually Pseudo-Split Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0034
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with forms of residually pseudo-split buildings. The proof rests on the fact that in every case, there is a Galois action of Γ‎ := GalL/K on Δ‎L whose fixed point building is ... More


Tits Indices

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0020
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces the notion of a Tits index and the notion of the relative Coxeter diagram of a Tits index. It first defines a Tits index, which can be anisotropic or isotropic, quasi-split or ... More


Descent in Buildings (AM-190)

Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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 ... More


Subbuildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0023
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a generalization of the typical notion of a subbuilding. It begins with the notation where Δ‎ is a building of type Π‎, and 𝐓 = (Π‎, Θ‎, A) is a Tits index of absolute type Π‎. ... More


Orthogonal Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0035
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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 ... More


Affine Fixed Point Buildings

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0027
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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 ... More


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