Explicit Solution of theSU(3)⊗SU(3)Algebra of Currents

Explicit formulas are given for various matrix elements of the axial-vector current in an arbitrary irreducible representation of the $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ algebra of currents. The formulas express such quantities as the renormalization $G_A$ of the axial-vector coupling constant, the strength $G^{*}$ of the axial-vector transition between $N$ and $N^{*}$, the $\frac{D}{F}$ ratio for the axial-vector current between states of the baryon octet, etc., in terms of the pair of integers that specify an irreducible representation of $\mathrm{SU}\left(3\right)\mathrm{}$.