Relations of representations of A_∞ and C_∞

In refs. [1—3] level one highest weight representations of complete infinite rank affine Lie algebra A_∞ were discussed. Since C_∞ is a subalgebra of A_∞, any representation of A_∞ induces a representation of C_∞. In this note, we discuss the relations of irreducible highest weight representations of A_∞ and C_∞.