Baryon Interpolating Fields via Double-Valued Octahedral Group Irreps — E8 Intelligence Research

FINDING: Baryon interpolating fields classified by double-valued irreps of octahedral group \\(O_h\\), constructed via Clebsch–Gordan coupling of three-quark spin-flavor states. | MATH: \\(SU(3)_\\text{flavor} \\otimes SU(2)_\\text{spin} \\supset O_h^\\text{double}\\); CG coefficients \\(\\langle j_1 m_1; j_2 m_2 | J M \\rangle\\) for \\(j_i \\in \\{1/2, 1\\}\\); subduction of \\(SU(3)\\) irreps \\(\\mathbf{8}, \\mathbf{10}, \\mathbf{27}\\) into \\(O_h\\) irreps \\(\\Gamma_4, \\Gamma_5, \\Gamma_6, \\Gamma_7, \\Gamma_8\\) (double-valued: \\(\\Gamma_6, \\Gamma_7\\) for spin-1/2; \\(\\Gamma_8\\) for spin-3/2). | CONNECTION: Octahedral group \\(O_h\\) is the full cubic point group (order 48), isomorphic to \\(S_4 \\times \\mathbb{Z}_2\\), whose double cover relates to binary octahedral group (order 48) — a crystallographic point group with root system \\(F_4\\) (24 roots). The subduction coefficients are integer/rational combinations of \\(\\sqrt{2}, \\sqrt{3}, \\sqrt{6}\\) — no golden ratio appears here, but the lattice discretization of QCD Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com