  An integrable structure behind Witten--Dijkgraaf--Verlinde--Verlinde (WDVV)
equations is identified with reduction of a Riemann-Hilbert problem for a
homogeneous GL(N, C) loop group. Reduction requires the dressing matrices to be
fixed points of a loop group automorphism of order two resulting in a
sub-hierarchy of gl(N,C) hierarchy containing only odd symmetry flows. The
model possesses Virasoro symmetry and imposing Virasoro constraints ensures
homogeneity property of the Darboux-Egoroff structure. Dressing matrices of the
reduced model provide solutions of the WDVV equations.
