@article {IOPORT.05909789,
    author       = {Lechtenfeld, Olaf and Schwerdtfeger, Konrad and Th\"urigen, Johannes},
    title        = {$N=4$ multi-particle mechanics, WDVV equation and roots.},
    year         = {2011},
    journal      = {SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]},
    volume       = {7},
    issn         = {1815-0659},
    pages        = {Paper 023, 21 p., electronic only},
    publisher    = {Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv},
    doi          = {10.3842/SIGMA.2011.023},
    abstract     = {Summary: We review the relation of $N=4$ superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, $F$ and $U$. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed.},
    identifier   = {05909789},
}