Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of type C_2

We study a pair of commuting difference operators arising from the elliptic solution of the dynamical Yang-Baxter equation of type C_2. The operators act on the space of meromorphic functions on the weight space of sp(4,C). We show that these operators can be identified with the system by van Diejen and by Komori-Hikami with special parameters. It turns out that our case can be related to the difference Lame operator (two-body Ruijsenaars operator) and thereby we diagonalize the system on the finite dimensional space spanned by the level one characters of the C_2^{(1)}-affine Lie algebra.