Buildings and Classical Groups

Garrett, Paul

doi:10.1007/978-94-011-5340-9

Cited by 150 publications

(140 citation statements)

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“…For each ω ∈ Ω(σ ω j ) there is a retraction from [s, ω) onto [s, ω j ) [Gt,4.2]. Let τ j (ω) be the inverse image of the chamber τ j under this retraction.…”

Section: Now It Follows From (4) That For Eachmentioning

confidence: 99%

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Torsion in Boundary Coinvariants and K-Theory for Affine Buildings

Robertson¹

2004

K-Theory

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Abstract. Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion free cocompact lattice in G. This article studies the coinvariants H 0 (Γ; C(Ω, Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H 0 (Γ; C(Ω, Z)) has finite order, with explicit bounds for the order.A similar statement applies to the K 0 group of the boundary crossed product C * -algebra C(Ω) ⋊ Γ. If the Tits system has type A 2 , exact computations are given, both for the crossed product algebra and for the reduced group C * -algebra.

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“…For each ω ∈ Ω(σ ω j ) there is a retraction from [s, ω) onto [s, ω j ) [Gt,4.2]. Let τ j (ω) be the inverse image of the chamber τ j under this retraction.…”

Section: Now It Follows From (4) That For Eachmentioning

confidence: 99%

“…Since the action of G is type preserving, it follows from [Gt,Theorem 17.3] that g ′ ∈ N trans . Moreover gv = g ′ v, for all v ∈ S. Let λ ω (g) = g ′ | A , the restriction of g ′ to A.…”

Section: Proof Let S ∈ ∆mentioning

confidence: 99%

Torsion in Boundary Coinvariants and K-Theory for Affine Buildings

Robertson¹

2004

K-Theory

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“…Tits's proof of the extension theorem is quite intricate. In spite of the fact that there have been three textbooks on buildings [1,2,3] and one textbook-length survey [4] prior to the book under review, none of these tries to prove the extension theorem or even to sketch a proof.…”

Section: The Classification Theoremmentioning

confidence: 99%

Book Review: The structure of spherical buildings

Brown¹

2005

Bull. Amer. Math. Soc.

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“…Let G be a torsion-free discrete group which acts cocompactly on a 2-dimensional euclidean building D [3,5,10]. For example, G may be any torsion-free lattice in PGL 3 ðFÞ, where F is a non-archimedean local field.…”

Section: Introductionmentioning

confidence: 99%