Commuting difference operators arising from the elliptic C⁽¹⁾₂-face model

We study a pair of commuting difference operators arising from the elliptic C⁽¹⁾₂-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C₂-type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp∧(4,C) is invariant under the action of the difference operators.