1203.4574 (Mehmet Koca et al.)

Quaterionic Construction of the W(F_4) Polytopes with Their Dual
Polytopes and Branching under the Subgroups B(B_4) and W(B_3)*W(A_1)    [PDF]

Mehmet Koca, Mudhahir Al-Ajmi, Nazife Koca

4-dimensional $F_{4} $ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group $W(F_{4})$ where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary \textbf{$W(F_{4})$} orbit under the Coxeter groups $W(B_{4} $ and $W(B_{3}) \times W(A_{1})$ have been presented. The role of group theoretical technique and the use of quaternions have been emphasized

View original: http://arxiv.org/abs/1203.4574