Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday
Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo
Almost duality for Saito structure and complex reflection groups II: the case of Coxeter and Shephard groups
Pages: 721 – 754
This article is a sequel to . It is known that the orbit spaces of the finite Coxeter groups and the Shephard groups admit two types of Saito structures without metric. One is the underlying structures of the Frobenius structures constructed by Saito  and Dubrovin . The other is the natural Saito structures constructed by Kato–Mano–Sekiguchi  and by Arsie–Lorenzoni . We study the relationship between these two Saito structures from the viewpoint of almost duality.
Frobenius structures, Saito structures, Coxeter groups, Shephard groups
2010 Mathematics Subject Classification
Primary 53D45. Secondary 20F55.
The first-named author is supported in part by JSPS KAKENHI Kiban-S 16H06337.
The second-named author is supported in part by JSPS KAKENHI Kiban-C 17K05228.
Received 28 April 2019
Accepted 8 June 2020
Published 11 November 2020