Immeubles affines: construction par les normes et étude des isométries

Parreau, Anne

doi:10.1090/conm/262/04180

Cited by 56 publications

(132 citation statements)

References 0 publications

Supporting

Mentioning

121

Contrasting

Unclassified

Order By: Relevance

“…Remark 6.2. Parreau gave an explicit description of the building associated to SL(2n, F) as the space of good norms on F 2n of determinant one [Par00]. It is possible to verify that, considering the affine building associated to Sp(2n, F) as a subbuilding of the affine building associated to SL(2n, F), the map π B corresponds to the map that associates to a point J ∈ X V the corresponding good norm η J (v) = (v, v) J .…”

Section: Fields With Valuation and The Projection To The Buildingmentioning

confidence: 99%

Maximal representations, non-Archimedean Siegel spaces, and buildings

Burger

Pozzetti

2017

Geom. Topol.

View full text Add to dashboard Cite

Abstract. Let F be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in Sp(2n, F). We show that ultralimits of maximal representations in Sp(2n, R) admit such a framing, and that all maximal framed representations satisfy a suitable generalization of the classical Collar Lemma. In particular this establishes a Collar Lemma for all maximal representations into Sp(2n, R). We then describe a procedure to get from representations in Sp(2n, F) interesting actions on affine buildings, and, in the case of representations admitting a maximal framing, we describe the structure of the elements of the group acting with zero translation length.

show abstract

Section: Fields With Valuation and The Projection To The Buildingmentioning

confidence: 99%

Maximal representations, non-Archimedean Siegel spaces, and buildings

Burger

Pozzetti

2017

Geom. Topol.

View full text Add to dashboard Cite

show abstract

“…Asymptotic sector-faces are necessarily parallel, the inverse is only true for sectors (see [10], Corollary 1.6). Asymptoticness is an equivalence relation as well.…”

Section: 12mentioning

confidence: 99%

“…A detailed study of R-buildings can be found in [10]. We list some results from that paper here for future reference.…”

Section: 12mentioning

confidence: 99%

(Non)-completeness of $ℝ$-buildings and fixed point theorems

Struyve

2011

Groups Geom. Dyn.

View full text Add to dashboard Cite

Abstract. We prove two generalizations of results of Bruhat and Tits involving metrical completeness and R-buildings. Firstly, we give a generalization of the Bruhat-Tits fixed point theorem also valid for non-complete R-buildings with the added condition that the group is finitely generated.Secondly, we generalize a criterion which reduces the problem of completeness to the wall trees of the R-building. This criterion was proved by Bruhat and Tits for R-buildings arising from root group data with valuation. Mathematics Subject Classification (2010). 51E24, 20F65.

show abstract

“…A detailed analysis of this definition and variations of it has been carried out by Anne Parreau in [5]. In particular, she shows that, if Conditions (A1), (A2), (A3) and (A4) are satisfied, then (A5 ) is equivalent to d being a distance function, together with (A5) If we have three apartements, such that each two apartments of these share a half-apartment, then the intersection of all three is non-empty.…”

Section: R-buildingsmentioning

confidence: 99%

“…(For two valua-tions v and v V (p,k)V (L,l) , the distance between both is defined as the length of the third side of a triangle in a Euclidean plane where two sides have length k and l, and with the angle between both sides π/n.) However by re-reading the proof in [5] of the equivalence of the various definitions of affine apartment systems, one sees that the weaker inequality d (u, v) ≤ 2(d(u, w) + d(w, v)) also suffices. This inequality is a direct consequence of Corollary 5.16.…”

Section: Building the Affine Apartment Systemmentioning

confidence: 99%

Two-Dimensional Ane R-Buildings De-ned by Generalized Polygons with Non-Discrete Valuation

Struyve¹,

Maldeghem²

2011

Pure and Applied Mathematics Quarterly

View full text Add to dashboard Cite

In this paper we complete the proof of the 'equivalence' of nondiscrete R-buildings of types A 2 and C 2 , with, respectively, projective planes and generalized quadrangles with non-discrete valuation, begun in [7]. We also complete the proof of the 'equivalence' of an affine building of rank 3 with a generalized polygon with discrete valuation (by proving this for generalized hexagons), begun in [14]. We also complement the main result of [13] by proving uniqueness up to scalar multiples of the weight sequences of polygons with non-discrete valuation. As an application, we produce some new explicitly defined non-discrete R-buildings, in particular a class of type A 2 with arbitrary residues.

show abstract

Immeubles affines: construction par les normes et étude des isométries

Cited by 56 publications

References 0 publications

Maximal representations, non-Archimedean Siegel spaces, and buildings

Maximal representations, non-Archimedean Siegel spaces, and buildings

(Non)-completeness of $ℝ$-buildings and fixed point theorems

Two-Dimensional Ane R-Buildings De-ned by Generalized Polygons with Non-Discrete Valuation

Contact Info

Product

Resources

About