On the geometry of V-systems

Abstract

We consider a complex version of the $\vee$-systems, which appeared in the theory of the WDVV equation. We show that the class of these systems is closed under the natural operations of restriction and taking the subsystems and study a special class of the $\vee$-systems related to generalized root systems and basic classical Lie superalgebras.

18 pages, 1 figure

References in corpus (1)

• On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations

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• Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
• 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
• WDVV solutions from orthocentric polytopes and Veselov systems
• Differential and Functional Identities for the Elliptic Trilogarithm
• Solutions of $B{C}_n$ Type of WDVV Equations