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arXiv math-ph/0105003math-phmath.MP
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轨迹配置和$\vee$系统

Locus configurations and $\vee$-systems

O. A. Chalykh, A. P. Veselov

摘要:

我们提出了一个新的家庭的轨迹配置,这是不相关的$\vee$ -系统,从而给出了答案的问题之一,在\cite{V1}之间的关系,广义量子Calogero-Moser系统和特殊解决方案的广义WDVV方程。作为副产品,我们有新的例子,双曲方程满足惠更斯原理在狭义阿达玛的意义。另一个结果是新的多参数家庭的$\vee$ -系统,它给出了新的解决方案的广义WDVV方程。

英文摘要:

We present a new family of the locus configurations which is not related to $\vee$-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 $\vee$-systems which gives new solutions of the generalised WDVV equation.

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