QUATERNIONIC CONSTRUCTION OF THE W(F4) POLYTOPES WITH THEIR DUAL POLYTOPES AND BRANCHING UNDER THE SUBGROUPS W(B4) AND W(B3) × W(A1)

2012/03/19 by Mehmet Koca, MEHMET KOCA, Mudhahir Al-Ajmi +3
Materials Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Branching (polymer chemistry) #Coxeter group #Finite Group Theory Research #Group (periodic table) #Orbit (dynamics) #Polytope #Quasicrystal Structures and Properties #Quaternion #math-ph #math.MP

paper · pdf · doi:10.1142/s0219887813500102

published as Int. J. Geom. Methods Mod. Phys,10, 1350010 (2013) · 26 pages, 10 figures

arxiv created 2012/03/19 · openalex publication_date 2013/04/03 · arxiv updated 2014/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Four-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 W(F 4 ) orbit under the Coxeter groups W(B 4 ) and W(B 3 ) × W(A 1 ) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

Citations

• Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
• INTEGRALS OF MOTION AND S-MATRIX OF THE (SCALED) T = Tc ISING MODEL WITH MAGNETIC FIELD