  We give a construction which produces a positive energy representation of the
affine Lie algebra of type A_n from the Stokes data of a solution of the
tt*-Toda equations of type A_n. The construction appears to play a role in
conformal field theory. We illustrate this with several examples: the fusion
ring, W-algebra minimal models (Argyres-Douglas theory), as well as
topological-antitopological fusion itself. (Minor typographical changes for
this version.)
