On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm.
Permutations with Kazhdan-Lusztig polynomial . With an appendix by Sara Billey and Jonathan Weed.
Platonic triangles of groups.
Poincaré polynomials for unitary reflection groups.
Polynomial invariants and harmonic functions related to exceptional regular polytopes.
Polynomials associated with dihedral groups.
Présentation de certains couples fischériens de type classique
Projective representations of reflection groups
Quiver varieties with multiplicities, Weyl groups of non-symmetric Kac-Moody algebras, and Painlevé equations.
Quotients of Coxeter complexes, fundamental groupoids and Regular Graphs.
Quotients of Polytopes and C-Groups.
Receding polar regions of a spherical building and the center conjecture
We introduce the notion of a polar region of a spherical building and use some simple observations about polar regions to give elementary proofs of various fundamental properties of root groups. We combine some of these observations with results of Timmesfeld, Balser and Lytchak to give a new proof of the center conjecture for convex chamber subcomplexes of thick spherical buildings.
Rectificatif à l'article «Présentation de certains couples fischériens de type classique»
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Representations of Coxeter Groups and Hecke Algebras.
Réseaux de Coxeter-Davis et commensurateurs
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...
Rigidity of skew-angled Coxeter groups.
Root systems for two dimensional complex reflection groups.
Schubert functions and the number of reduced words of permutations.
Singularités génériques des variétés de Schubert covexillaires
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.