Abstract
In this paper, we prove that, given any integers d,e,r and r′, and a prime p not dividing de, any two blocks of the complex reflection groups G(de, e, r) and G(de, e, r′) with the same p-weight are perfectly isometric.
| Original language | English |
|---|---|
| Pages (from-to) | 260-292 |
| Number of pages | 33 |
| Journal | Journal of Algebra |
| Volume | 558 |
| Early online date | 15 May 2019 |
| DOIs | |
| Publication status | Published - 15 Sept 2020 |
Bibliographical note
Acknowledgements.The authors are grateful to M. Broué for asking the question this article settles, at the end of a talk given by the first author at the Beijing Center for Mathematical Research during the Third International Symposium on Groups, Algebras and Related Topics, celebrating the 50th anniversary of the Journal of Algebra. Part of this work was done at the CIRM in Luminy during a research in pairs stay. The authors wish to thank the CIRM gratefully for their financial and logistical support. The first author is supported by Agence Nationale de la Recherche Projet GeRepMod ANR-16-CE40-00010-01. The second author also acknowledges financial support from the Engineering and Physical Sciences Research Council grant Combinatorial Representation Theory EP/M019292/1.Keywords
- Perfect isometries
- Complex reflection groups
