Conjugation is Inversion Weighted by the Norm: A Unifying Identity for the Three-Field Model (Research Note 12)

Abstract

Research Note 12 of the INDYNA program. This note studies the interplay of the Galois involution σ, the field norm, and coupling inversion g → 1/g in the conjugate-shell family: the three operations generate the symmetry group of the phase diagram, and their invariants classify the crossings. Part of the numbered series (Notes 7–15) on the exactly solvable spectral theory of icosahedral networks.