Linear Independence for A₁⁽¹⁾ by Using C₂⁽¹⁾

In the previous paper, the authors proved linear independence of the combinatorial spanning set for standard C_⁽¹⁾-module L(kΛ₀) by establishing a connection with the combinatorial basis of Feigin-Stoyanovsky's type subspace W(kΛ₀) of C₂⁽¹⁾-module L(kΛ₀). In this note we extend this argument for C₁⁽¹⁾ A₁⁽¹⁾ to all standard A₁⁽¹⁾-modules L(Λ). In the proof we use a coefficient of an intertwining operator of the type L(Λ₂)L(Λ₁)\ L(Λ₁) for standard C₂⁽¹⁾-modules.