ABSTRACT
We verify the Broué–Malle–Rouquier (BMR) freeness for cyclotomic Hecke algebras associated with complex reflection groups G17, G18, G19 in the Shephard–Todd classification. Together with results of Ariki, Ariki–Koike, Broué–Malle, Marin, Marin–Pfeiffer, and Chavli, this settled affirmatively the BMR freeness conjecture. Our verification is inspired by Bergman’s diamond lemma and requires 1GB memory and 5 days calculation on a PC.
2010 Mathematics Subject Classification:
5. Appendix: The sequences
Acknowledgments
The major part of the work was carried out at Caffe Strada when the author visited University of California Berkeley for Berkeley-Tokyo Summer School “Geometry, Representation Theory and Mathematical Physics” in August, 2017. The author thanks Toshitake Kohno for giving him an opportunity.