Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 3

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

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n3.a12


Yukiko Konishi (Department of Mathematics, College of Liberal Arts, Tsuda University, Toyko, Japan)

Satoshi Minabe (Department of Mathematics, Tokyo Denki University, Tokyo, Japan)


This article is a sequel to [6]. 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 [12] and Dubrovin [4]. The other is the natural Saito structures constructed by Kato–Mano–Sekiguchi [5] and by Arsie–Lorenzoni [1]. 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