Locus configurations and $\vee$-systems
O.A.Chalykh, A.P.Veselov
TL;DR
This paper introduces new locus configurations unrelated to $ $-systems, providing insights into quantum Calogero-Moser systems, WDVV equations, and Huygens' principle, along with new $ $-system solutions.
Contribution
It presents novel locus configurations and $ $-systems, addressing open questions about their relations to quantum systems and WDVV equations.
Findings
New locus configurations not related to $ $-systems.
New solutions to the generalized WDVV equations.
Examples of hyperbolic equations satisfying Huygens' principle.
Abstract
We present a new family of the locus configurations which is not related to -systems thus giving the answer to one of the questions raised in \cite{V1} about the relation between the generalised quantum Calogero-Moser systems and special solutions of the generalised WDVV equations. As a by-product we have new examples of the hyperbolic equations satisfying the Huygens' principle in the narrow Hadamard's sense. Another result is new multiparameter families of -systems which gives new solutions of the generalised WDVV equation.
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