2 citations · 4 across the 6 of their papers we have counts for
6 papers
Fundamental polytope for the isometry group of an alcove
Lucas Seco, Arthur Garnier, Karl-Hermann Neeb
A fundamental alcove is a tile in a paving of a vector space by an affine reflection group . Its geometry encodes essential features of $W_{\mat…
Fundamental polytope for the Weyl group acting on a maximal torus of a compact Lie group
Arthur Garnier
We provide a fundamental domain for the action of the finite Weyl group on a maximal torus of a compact Lie group of the corresponding type. The general situation is reduced to the…
Motion equations in a Kerr-Newman-de Sitter spacetime: some methods of integration and application to black holes shadowing in Scilab
Arthur Garnier
In this paper, we recall some basic facts about the Kerr--Newman--(anti) de Sitter (KNdS) spacetime and review several formulations and integration methods for the geodesic equatio…
Equivariant triangulations of tori of compact Lie groups and hyperbolic extension to non-crystallographic Coxeter groups
Arthur Garnier
Given a simple connected compact Lie group and a maximal torus of , the Weyl group naturally acts on . First, we use the combinatorics of the (extended)…
Dirichlet-Voronoi domain and injectivity radius of flag manifolds -- equivariant cell structure on
Arthur Garnier
In the first part of this work, we study Dirichlet--Voronoi domains for discrete isometry groups of Riemannian manifolds, in view of constructing cell structures on homogeneous (co…
Cellularization for exceptional spherical space forms and the flag manifold of
Rocco Chirivi, Arthur Garnier, Mauro Spreafico
We construct an explicit equivariant cellular decomposition of the -sphere with respect to binary polyhedral groups, and describe the associated cellular homology chain com…