Locus configurations and $\vee$-systems

Abstract

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.

12 pages

References in corpus (1)

• On geometry of a special class of solutions to generalised WDVV equations

Cited by in corpus (22)

• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Superconformal mechanics
• N=4 mechanics, WDVV equations and roots
• Many-particle mechanics with D(2,1;alpha) superconformal symmetry
• N=4 superconformal n-particle mechanics via superspace
• Generalized Lame operators
• Weyl groups and Elliptic Solutions of the WDVV equations
• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• $\mathcal{N}=4$ supersymmetric mechanics on curved spaces
• On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations
• Superconformal Quantum Mechanics from M2-branes
• Coxeter discriminants and logarithmic Frobenius structures
• Duality for Jacobi group orbit spaces and elliptic solutions of the WDVV equations
• Trigonometric $\vee$-systems and solutions of WDVV equations
• Deformed Calogero--Moser operators and ideals of rational Cherednik algebras
• Purely non-local Hamiltonian formalism, Kohno connections and $\vee$-systems
• Differential and Functional Identities for the Elliptic Trilogarithm
• Bispectrality of $A{G}_2$ Calogero-Moser-Sutherland system
• Legendre transforms for type $A_n$ and $B_n$ $\vee$-systems
• Solutions of $B{C}_n$ Type of WDVV Equations
• N=4 Mechanics, WDVV Equations and Polytopes
• Baker-Akhiezer function for the deformed root system $BC(l,1)$ and bispectrality