Solutions of $BC_{n}$ Type of WDVV Equations

Alkadhem, Maali; Antoniou, Georgios; Feigin, Misha

doi:10.48550/arxiv.2002.02900

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…The proof of the next lemma is similar to the proof of [17, Lemma 1] in the rational case (see also [1]).…”

Section: Restriction Of Trigonometric Solutions Of Wdvv Equationsmentioning

confidence: 79%

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Trigonometric $\vee$-systems and solutions of WDVV equations

Alkadhem,

Feigin

2020

Preprint

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We consider a class of trigonometric solutions of WDVV equations determined by collections of vectors with multiplicities. We show that such solutions can be restricted to special subspaces to produce new solutions of the same type. We find new solutions given by restrictions of root systems, as well as examples which are not of this form. Further, we consider a closely related notion of a trigonometric ∨-system and we show that their subsystems are also trigonometric ∨-systems. Finally, while reviewing the root system case we determine a version of (generalised) Coxeter number for the exterior square of the reflection representation of a Weyl group.

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“…The proof of the next lemma is similar to the proof of [17, Lemma 1] in the rational case (see also [1]).…”

Section: Restriction Of Trigonometric Solutions Of Wdvv Equationsmentioning

confidence: 79%

“…In the case of BC n we get a family of solutions depending on n + 3 parameters which can be specialized to Pavlov's (n+1)-parametric family from [26]. A related multi-parameter deformation of BC n solutions (1.2) when Q depends on x variables only was obtained in [1] by similar methods.…”

Section: Introductionmentioning

confidence: 99%

Trigonometric $\vee$-systems and solutions of WDVV equations

Alkadhem,

Feigin

2020

Preprint

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“…where R(X, Y ) and R(X, Y ) are Riemannian curvature tensors of ∇ = ∇ (1) and ∇ = ∇ (−1) respectively. When α = 0, (2.8) is just (2.4).…”

Section: Statistical Structure and Sectional K-curvaturementioning

confidence: 99%

“…There is large amount of work solving the potential WDVV equation (3.24), we only mention a solution related to BC n root system in a recent paper of Alkadhem-Antoniou-Feigin [1].…”

Section: Frobenius Structurementioning

confidence: 99%

Affine geometry and Frobenius algebra

Liu¹,

Xu²,

Zhi³

2021

Preprint

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The associativity of the multiplication on a Frobenius manifold is equivalent to the WDVV equation of a symmetric cubic form in flat coordinates. Frobenius manifold could be regarded a very special type of statistical manifold. There is a natural commutative product on each tangent space of a statistical manifold. We show that it is associative, hence making it into a manifold with Frobenius algebra structure, if and only if the sectional K-curvature vanishes. In other words, WDVV equation is equivalent to zero sectional K-curvature. This gives a curvature interpretation for WDVV equation.

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Solutions of $BC_{n}$ Type of WDVV Equations

Abstract: We give a family of solutions of Witten-Dijkgraaf-Verlinde-Verlinde equations in n-dimensional space. It is defined in terms of BC n root system and n + 2 independent multiplicity parameters. We also apply these solutions to define some N = 4 supersymmetric mechanical systems.

Cited by 2 publications

References 15 publications

Trigonometric $\vee$-systems and solutions of WDVV equations

Trigonometric $\vee$-systems and solutions of WDVV equations

Affine geometry and Frobenius algebra

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