Almost duality for Saito structure and complex reflection groups. Issue 1 (13th March 2018)

• Record Type: Journal Article
• Authors: Konishi, Yukiko; Minabe, Satoshi; Shiraishi, Yuuki
• Is Part Of: Journal of integrable systems. Volume 3:Issue 1(2018)
• Publication Date: 2018-03-13
• Subjects: Frobenius structures -- Saito structures -- complex reflection groups; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyy003
• Languages: English
• ISSNs: 2058-5985

Abstract

Abstract: 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. Communicated by: Alexander Veselov