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Almost duality for Saito structure and complex reflection groups. (English) Zbl 1397.37081

Summary: We reformulate Dubrovin’s almost duality of the Frobenius structure to the setting of the Saito structures without metric. Then, we formulate and study the existence and uniqueness problem of the natural Saito structure on the orbit spaces of finite complex reflection groups from the viewpoint of the almost duality. We give a complete answer to the problem for the irreducible groups.

MSC:

37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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