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The rings of n-dimensional polytopes

Identifieur interne : 000797 ( Main/Exploration ); précédent : 000796; suivant : 000798

The rings of n-dimensional polytopes

Auteurs : L. Hkov [Canada] ; M. Larouche [Canada] ; J. Patera [Canada]

Source :

RBID : ISTEX:3A0034A1847B07D53118F760AB5D7CDA5ACB1E75

English descriptors

Abstract

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G-polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.

Url:
DOI: 10.1088/1751-8113/41/49/495202


Affiliations:


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Le document en format XML

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<term>Cartan matrices</term>
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<term>Subsequent columns</term>
<term>Such questions</term>
<term>Suitable choice</term>
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<term>Symmetrized powers</term>
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<term>Symmetry groups</term>
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<term>Various degrees</term>
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<term>Anomaly</term>
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<term>Anomaly numbers</term>
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<term>Cartan matrices</term>
<term>Check marks</term>
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<term>Complete list</term>
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<term>Congruence classes</term>
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<term>Harmonic analysis</term>
<term>Higher indices</term>
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<term>Many places</term>
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<term>Symmetry group</term>
<term>Symmetry groups</term>
<term>Theor</term>
<term>Various degrees</term>
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<div type="abstract">Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G-polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.</div>
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