In the SU(3) lattice gauge theory the recursion relations of coefficients of the character expansion are derived through the Schwinger–Dyson equation for the ensemble average containing multilink variables. The variables form two kinds of recursion relations which correspond to two independent integers λ and μ of the SU(3) (λμ) representation of the Young tableau. The property of the recursion relations in comparison with those of the U(1) and SU(2) groups is discussed.

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