Flag-transitive extensions of dual affine spaces.
Formules de Matsushima, de Garland et propriété (T) pour des groupes agissant sur des espaces symétriques ou des immeubles
Frobenius collineations in finite projective planes.
Generalisations of the Tits representation.
Gluing two affine spaces.
Group actions on twin buildings.
Groups acting on products of trees, tiling systems and analytic -theory.
Group-theoretic compactification of Bruhat–Tits buildings
Immeubles de Tits triangulaires exotiques
Kac-Moody groups, hovels and Littelmann paths
We give the definition of a kind of building for a symmetrizable Kac-Moody group over a field endowed with a discrete valuation and with a residue field containing . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if , the geodesic segments...
Local to global sturcute in twin buildings.
Macdonald formula for spherical functions on affine buildings
In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.
Metric characterizations of spherical and Euclidean buildings.
Moufang buildings and twin buildings.
On compression of Bruhat--Tits buildings.
On groups with root system of type .
On some flag-transitive non-classical -geometries. II.
On the Haagerup inequality and groups acting on -buildings
Let be a group endowed with a length function , and let be a linear subspace of . We say that satisfies the Haagerup inequality if there exists constants such that, for any , the convolutor norm of on is dominated by times the norm of . We show that, for , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on . If is a word length function on a finitely generated group , we show that,...
On the loop inequality for euclidean buildings
We give an estimate for the number of closed loops of given length in the 1-skeleton of a thick euclidean building. This kind of estimate can be used to prove the (RD) property for the subspace of radial functions on groups, as shown in the paper by A. Valette [same issue].
On Veldkamp lines.