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• W3128995802 abstract "Rational solutions of the Witten–Dijkgraaf–Verlinde–Verlinde (or WDVV) equations of associativity are given in terms of configurations of vectors, which satisfy certain algebraic conditions known as ⋁-conditions [A. P. Veselov, Phys. Lett. A 261, 297–302 (1999)]. The simplest examples of such configurations are the root systems of finite Coxeter groups. In this paper, conditions are derived that ensure that an extended configuration—a configuration in a space one-dimension higher—satisfies these ⋁-conditions. Such a construction utilizes the notion of a small orbit, as defined in Serganova [Commun. Algebra, 24, 4281–4299 (1996)]. Symmetries of such resulting solutions to the WDVV equations are studied, in particular, Legendre transformations. It is shown that these Legendre transformations map extended-rational solutions to trigonometric solutions, and for certain values of the free data, one obtains a transformation from extended ⋁-systems to the trigonometric almost-dual solutions corresponding to the classical extended affine Weyl groups." @default.
• W3128995802 created "2021-02-15" @default.
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• W3128995802 date "2021-02-01" @default.
• W3128995802 modified "2023-09-27" @default.
• W3128995802 title "Extended ⋁-systems and trigonometric solutions to the WDVV equations" @default.
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• W3128995802 doi "https://doi.org/10.1063/5.0024108" @default.
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