  We prove that the total descendant potential functions of the theory of
Fan-Jarvis-Ruan-Witten for D_4 with symmetry group <J> and D_4^T with symmetry
group G_{max}, respectively, are both tau-functions of the D_4
Kac-Wakimoto/Drinfeld-Sokolov hierarchy. This completes the proof, begun in
[FJR], of the Witten Integrable Hierarchies Conjecture for all simple (ADE)
singularities.
