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)

Abstract

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

26 pages, 10 figures

References in corpus (2)

• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• 4D-Polytopes and Their Dual Polytopes of the Coxeter Group $W(A_4)$ Represented by Quaternions