Regular lattice polytopes and root systems

Montagard, Pierre-Louis; Ressayre, Nicolas

doi:10.1112/blms/bdn120

Cited by 2 publications

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References 2 publications

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“…Using [15], we know that the fixed polytope is an n-simplex. Moreover, the n + 1 weights on the vertices are given by (n + 1)ω 1 and (n + 1)(ω 1 − α), where α ∈ Comp(eP 1 , P n , H).…”

Section: 2mentioning

confidence: 99%

“…It seems natural that the projection which provides the minimal bandwidth has to be linked, in some sense, to the simmetries of the polytope ∆(X). In the case of RH varieties, ∆(X) is given by the Coxeter polytope associated to the marked Dynkin diagram (see [15] for an introduction to the topic) and the symmetries of this polytope are given by some hyperplanes h i orthogonal to certain elements α i (called simple roots) of the root system Φ(G, H). Then we can restate the problem in terms of convex geometry.…”

Section: Introductionmentioning

confidence: 99%

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Minimal bandwidth $\mathbb{C}^*$-actions on generalized Grassmannians

Franceschini¹

2020

Preprint

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The bandwidth of a C * -action of a polarized pair (X, L) is a natural measure of its complexity. In this paper we study C * -actions on rational homogeneous spaces, determining which provide minimal bandwidth. We prove that the minimal bandwidth is linked to the smallest coefficient of the fundamental weight, in the base of simple roots, which describes the variety as a marked Dynkin diagram. As a direct application we recover the (co)homology groups of the Cayley plane E6(1). Contents 1. Introduction 1 2. Preliminaries 5 3. Downgradings along simple roots and associated C * -actions 9 4. Minimal bandwidth C * -actions on RH varieties 11 Appendix A. (Co)homology groups of the complex Cayley plane 19 References 20

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Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimal bandwidth $\mathbb{C}^*$-actions on generalized Grassmannians

Franceschini¹

2020

Preprint

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Minimal bandwidth for $${\mathbb C}^*$$-actions on generalized Grassmannians

Franceschini

2022

Rend. Circ. Mat. Palermo, II. Ser

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The bandwidth of a $${\mathbb C}^*$$ C ∗ -action of a polarized pair (X, L) is a natural measure of its complexity. In this paper, we study $${\mathbb C}^*$$ C ∗ -actions on rational homogeneous spaces, determining which provide minimal bandwidth. We prove that the minimal bandwidth is linked to the smallest coefficient of the fundamental weight, in a base of simple roots, which describes the variety as a marked Dynkin diagram. As a direct application of the results we study the Chow groups of the Cayley plane $$\mathrm{E}_6(6)$$ E 6 ( 6 ) .

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Regular lattice polytopes and root systems

Cited by 2 publications

References 2 publications

Minimal bandwidth $\mathbb{C}^*$-actions on generalized Grassmannians

Minimal bandwidth $\mathbb{C}^*$-actions on generalized Grassmannians

Minimal bandwidth for $${\mathbb C}^*$$-actions on generalized Grassmannians

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