2001/11/27 by Henrik Aratyn, Johan van de Leur
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #nlin.SI
published as Theor.Math.Phys. 134 (2003) 14-26; Teor.Mat.Fiz. 134 (2003) 18-31 · 14 pgs, contribution to Needs 2001 conference proceedings
arxiv created 2001/11/27 · arxiv updated 2009/11/30
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.