Let be the comer-transfer-matrix Hamiltonian for the six-vertex model in the anti-ferroelectric regime. It acts on the infinite tensor product W = V x V x V x ..., where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra U(q)(sl(2)). We observe that H is the derivation of U(q)(sl(2)), and conjecture that the eigenvectors of H form the level-1 vacuum representation of U(q)(sl(2)). We report on checks in support of our conjecture.