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pro vyhledávání: '"Garnier, Arthur"'
A fundamental alcove $\mathcal{A}$ is a tile in a paving of a vector space $V$ by an affine reflection group $W_{\mathrm{aff}}$. Its geometry encodes essential features of $W_{\mathrm{aff}}$, such as its affine Dynkin diagram $\widetilde{D}$ and fund
Externí odkaz:
http://arxiv.org/abs/2501.01654
Autor:
Garnier, Arthur
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 adjoint case and, from the perspective of root data, this problem can
Externí odkaz:
http://arxiv.org/abs/2409.16483
Autor:
Garnier, Arthur
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics, and the Bertotti-Robinson-lik
Externí odkaz:
http://arxiv.org/abs/2401.15809
Autor:
Garnier, Arthur
Publikováno v:
Classical and Quantum Gravity, Volume 40, Number 13 (2023)
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 equation of a test particle in such a spacetime. In particular, we introduce
Externí odkaz:
http://arxiv.org/abs/2307.04073
Autor:
Garnier, Arthur
Given a simple connected compact Lie group $K$ and a maximal torus $T$ of $K$, the Weyl group $W=N_K(T)/T$ naturally acts on $T$. First, we use the combinatorics of the (extended) affine Weyl group to provide an explicit $W$-equivariant triangulation
Externí odkaz:
http://arxiv.org/abs/2105.00237
Autor:
Garnier, Arthur
We present some perspectives in the construction of explicit cell structures on real flag manifolds, equivariant with respect to the (free) action of the Weyl group. Such structures could be obtained from Dirichlet-Voronoi fundamental domains associa
Externí odkaz:
http://arxiv.org/abs/2011.06338
We construct an explicit equivariant cellular decomposition of the $(4n-1)$-sphere with respect to binary polyhedral groups, and describe the associated cellular homology chain complex. As a corollary of the binary octahedral case, we deduce an $\mat
Externí odkaz:
http://arxiv.org/abs/2006.14417
Akademický článek
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Autor:
Garnier, Arthur
Using three-dimensional spherical space forms, Chirivi, Spreafico and the author found a cellular structure on the flag manifold SO(3)/S(O(1) 3), equivariant with respect to the action of the Weyl group W = S3. In this note, we give some Riemannian g
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::8fd1542de4fd5c6c6461a0e0e0f5b739
https://hal.archives-ouvertes.fr/hal-03372068/file/Riemannian_corrected.pdf
https://hal.archives-ouvertes.fr/hal-03372068/file/Riemannian_corrected.pdf