  We give an explicit description of the vector bundle of WZW conformal blocks
on elliptic curves with marked points as subbundle of a vector bundle of Weyl
group invariant vector valued theta functions on a Cartan subalgebra. We give a
partly conjectural characterization of this subbundle in terms of certain
vanishing conditions on affine hyperplanes. In some cases, explicit calculation
are possible and confirm the conjecture. The Friedan--Shenker flat connection
is calculated, and it is shown that horizontal sections are solutions of
Bernard's generalization of the Knizhnik--Zamolodchikov equation.
