Symmetries of the WDVV Equations

We investigate the symmetry structure of the WDVV equations. We obtain an r-parameter group of symmetries, where r=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\frac{1}{2}$$ \end{document}(n2+7n+4)+⌊n/2⌋. Moreover, it is proved that for n=3 and n=4 these comprise all symmetries. We determine a subgroup, which defines an SL2-action on the space of solutions. For the special case n=3 this action is compared to the SL2-symmetry of the Chazy equation. We construct similar solutions in the cases n=4 and n=5.