Konishi, Yukiko; Minabe, Satoshi; Shiraishi, Yuuki Almost duality for Saito structure and complex reflection groups. (English) Zbl 1397.37081 J. Integrable Syst. 3, Article ID xyy003, 48 p. (2018). 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. Cited in 1 ReviewCited in 10 Documents 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.) Keywords:Frobenius structure; Saito structure; complex reflection group PDFBibTeX XMLCite \textit{Y. Konishi} et al., J. Integrable Syst. 3, Article ID xyy003, 48 p. (2018; Zbl 1397.37081) Full Text: DOI arXiv