Induced Representations of Strong Coupling Groups

Mackey's method of induced representations is applied to the strong coupling group G = K·T, where K is compact and T is Abelian, to obtain the general irreducible representations. The form of the meson-isobar-isobar couplings is obtained by reducing these, with the use of the Peter-Weyl theorem, to irreducible representations of the compact subgroup K. The results are applied to the cases: pseudoscalar octet mesons, K = SU2 ⊗ SU3, T = T24, and SU6 35-plet mesons, K = SU6, T = T35. Explicit representations are obtained which are consistent with mass formulas M∝f2(μ)−58j(j+1) and M∝G2 in the respective cases.