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.
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics