Noncrystallographic Coxeter group H4 in E8

Mehmet Koca; Ramazan Koc; Muataz Al-Barwani

doi:10.1088/0305-4470/34/50/303

Noncrystallographic Coxeter group H₄ in E₈

Mehmet Koca^*, Ramazan Koc, Muataz Al-Barwani

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

The E₈ lattice is constructed in terms of icosians by matching two sets of F₄ lattices described by quaternions. Embedding the noncrystallographic group H₄ into the Weyl group W(E₈) has been described using matrix generators with an emphasis on the relevant Coxeter elements. The conjugacy classes of H₄ in terms of quaternions and the characters of the two four-dimensional irreducible representations are explicitly calculated.

Original language	English
Pages (from-to)	11201-11213
Number of pages	13
Journal	Journal of Physics A: Mathematical and General
Volume	34
Issue number	50
DOIs	https://doi.org/10.1088/0305-4470/34/50/303
Publication status	Published - Dec 21 2001

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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abstract = "The E8 lattice is constructed in terms of icosians by matching two sets of F4 lattices described by quaternions. Embedding the noncrystallographic group H4 into the Weyl group W(E8) has been described using matrix generators with an emphasis on the relevant Coxeter elements. The conjugacy classes of H4 in terms of quaternions and the characters of the two four-dimensional irreducible representations are explicitly calculated.",

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AU - Al-Barwani, Muataz

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N2 - The E8 lattice is constructed in terms of icosians by matching two sets of F4 lattices described by quaternions. Embedding the noncrystallographic group H4 into the Weyl group W(E8) has been described using matrix generators with an emphasis on the relevant Coxeter elements. The conjugacy classes of H4 in terms of quaternions and the characters of the two four-dimensional irreducible representations are explicitly calculated.

AB - The E8 lattice is constructed in terms of icosians by matching two sets of F4 lattices described by quaternions. Embedding the noncrystallographic group H4 into the Weyl group W(E8) has been described using matrix generators with an emphasis on the relevant Coxeter elements. The conjugacy classes of H4 in terms of quaternions and the characters of the two four-dimensional irreducible representations are explicitly calculated.

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Noncrystallographic Coxeter group H₄ in E₈

Abstract

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