The 785 conjugacy classes of rational elements of finite order in 𝐸₈

McKay, W. G.; Moody, R. V.; Patera, J.; Pianzola, A.

doi:10.1090/conm/110/1079104

Cited by 3 publications

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“…The points of the fundamental domain, representing such elements, are listed in Tables 1-6 for compact simple Lie groups of rank 2 and 3. Generally such points are not found in the literature except for the group E 8 , see [38].…”

Section: Orbit Functions At Rational Pointsmentioning

confidence: 91%

Orbit Functions

Klimyk¹

2006

SIGMA

192

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Abstract. In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space E n are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space E n . Orbit functions are solutions of the corresponding Laplace equation in E n , satisfying the Neumann condition on the boundary of F . Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points.

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Section: Orbit Functions At Rational Pointsmentioning

confidence: 91%

Orbit Functions

Klimyk¹

2006

SIGMA

192

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Faces of root polytopes in all dimensions

Szajewska

2016

Acta Cryst Sect A

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In this paper the root polytopes of all finite reflection groups W with a connected Coxeter-Dynkin diagram in {\bb R}^n are identified, their faces of dimensions 0 ≤ d ≤ n - 1 are counted, and the construction of representatives of the appropriate W-conjugacy class is described. The method consists of recursive decoration of the appropriate Coxeter-Dynkin diagram [Champagne et al. (1995). Can. J. Phys. 73, 566-584]. Each recursion step provides the essentials of faces of a specific dimension and specific symmetry. The results can be applied to crystals of any dimension and any symmetry.

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Embeddings of P G L 2 ( 31 ) and S L 2 ( 32 ) in E 8

Griess¹

1998

Duke Math. J.

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The 785 conjugacy classes of rational elements of finite order in 𝐸₈

Cited by 3 publications

References 0 publications

Orbit Functions

Orbit Functions

Faces of root polytopes in all dimensions

Embeddings of P G L 2 ( 31 ) and S L 2 ( 32 ) in E 8

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