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646
Affine buildings for dihedral groups
, 2008
"... We construct rank 2 thick nondiscrete affine buildings associated with an arbitrary finite dihedral group. 1 ..."
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Cited by 4 (1 self)
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We construct rank 2 thick nondiscrete affine buildings associated with an arbitrary finite dihedral group. 1
AXIOMS OF AFFINE BUILDINGS
, 2009
"... We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that being an affine building is independent of the metric structure of the space. ..."
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We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that being an affine building is independent of the metric structure of the space.
Kostant convexity for affine buildings
, 2008
"... Abstract. We prove an analogue of Kostants convexity theorem for thick affine buildings and give an application for groups with affine BNpair. Recall that there are two natural retractions of the affine building onto a fixed apartment A: The retraction r centered at an alcove in A and the retractio ..."
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Abstract. We prove an analogue of Kostants convexity theorem for thick affine buildings and give an application for groups with affine BNpair. Recall that there are two natural retractions of the affine building onto a fixed apartment A: The retraction r centered at an alcove in A
Isotropic random walks on affine buildings
 Ann. Inst. Fourier (Grenoble
, 2005
"... Abstract. Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where Ã ..."
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Cited by 8 (2 self)
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Abstract. Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where
Tropical Geometry and Affine Buildings
, 2007
"... We will discuss the case of dimension 2 and higher in this lecture. This is joint work with ..."
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We will discuss the case of dimension 2 and higher in this lecture. This is joint work with
Expanders and the Affine Building of Sp n
, 2008
"... For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Sp n(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is nonamena ..."
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For n ≥ 2 and a local field K, let ∆n denote the affine building naturally associated to the symplectic group Sp n(K). We compute the spectral radius of the subgraph Yn of ∆n induced by the special vertices in ∆n, from which it follows that Yn is an analogue of a family of expanders and is nonamenable.
DISTANCE IN THE AFFINE BUILDINGS OF SLn AND Spn
 INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 (2008), #A48
, 2008
"... For a local field K and n ≥ 2, let Ξn and ∆n denote the affine buildings naturally associated to the special linear and symplectic groups SLn(K) and Spn(K), respectively. We relate the number of vertices in Ξn (n ≥ 3) close (i.e., gallery distance 1) to a given vertex in Ξn to the number of chambers ..."
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Cited by 1 (0 self)
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For a local field K and n ≥ 2, let Ξn and ∆n denote the affine buildings naturally associated to the special linear and symplectic groups SLn(K) and Spn(K), respectively. We relate the number of vertices in Ξn (n ≥ 3) close (i.e., gallery distance 1) to a given vertex in Ξn to the number
Spherical harmonic analysis on affine buildings
 Mathematische Zeitschrift
, 2006
"... Abstract. Let X be a locally finite regular affine building with root system R. There is a commutative algebra A spanned by averaging operators Aλ, λ ∈ P +, acting on the space of all functions f: VP → C, where VP is in most cases the set of all special vertices of X, and P + is a set of dominant co ..."
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Cited by 12 (6 self)
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Abstract. Let X be a locally finite regular affine building with root system R. There is a commutative algebra A spanned by averaging operators Aλ, λ ∈ P +, acting on the space of all functions f: VP → C, where VP is in most cases the set of all special vertices of X, and P + is a set of dominant
MVPOLYTOPES VIA AFFINE BUILDINGS
, 903
"... Abstract. For an algebraic group G, Anderson originally defined the notion of MVpolytopes in [And03], images of MVcycles, defined in [MV07], under the moment map of the corresponding affine Grassmannian. It was shown by Kamnitzer in [Kam07] and [Kam05] that these polytopes can be described via tro ..."
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combinatorial construction of the MVpolytopes using LSgalleries. In addition we link this construction to the retractions of the affine building and the BottSamelson variety corresponding to G. This leads to a definition of MVpolytopes not involving the tropical Plücker relations. Herefore it provides a
NONDISCRETE AFFINE BUILDINGS AND CONVEXITY
, 2009
"... A ne buildings are in a certain sense analogs of symmetric spaces. It is therefore natural to try to nd analogs of results for symmetric spaces in the theory of buildings. In this paper we prove a version of Kostant's convexity theorem for thick nondiscrete a ne buildings. Kostant proves tha ..."
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A ne buildings are in a certain sense analogs of symmetric spaces. It is therefore natural to try to nd analogs of results for symmetric spaces in the theory of buildings. In this paper we prove a version of Kostant's convexity theorem for thick nondiscrete a ne buildings. Kostant proves
Results 1  10
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