  We discuss a class of two-point functions on the torus of primary operators
in the SU(2) Wess-Zumino-Witten model at integer level k. In particular, we
construct an explicit expression for the current blocks of the
spin-k/2-spin-k/2 torus two-point functions for all k. We first examine the
factorization limits of the proposed current blocks and test their monodromy
properties. We then prove that the current blocks solve the corresponding
Knizhnik-Zamolodchikov-like differential equations using the method of Mathur,
Mukhi and Sen.
