Fermions and Yukawa Couplings from the Representation Theory of 2I∗

We show that the Yukawa couplings of the SO(3,3) matrix model on P^3 = S^3/2I* are determined by the representation theory of the binary icosahedral group 2I*, with no free parameters. The Higgs field is identified with the rho_2 representation of A_5 (dim 3) -- the same representation that carries the three generations and determines the fine-structure constant. The Yukawa vertex is mediated exclusively through the rho_8 component of the left-handed fermion (the Pati-Salam quartet), not through the rho_6 component (the SU(2)_L doublet). The coupling channel rho_8 x rho_2 -> rho_9 has multiplicity one, making the Yukawa coupling unique up to overall normalisation. The Clebsch-Gordan coefficients are the standard SU(2) CG coefficients, with all CG^2 rational multiples of 1/10. The tree-level Yukawa gives exactly equal masses for all three generations (by CG orthogonality). The one-loop orbifold correction is also democratic (by Schur's lemma). The fermion mass hierarchy must therefore arise from the Higgs VEV, which breaks the A_5 symmetry. The Molien series shows that no A_5-specific quartic potential exists; the VEV direction is determined by the degree-6 icosahedral invariant I_6.