## The BMR freeness conjecture for the 2-reflection groups

HTML articles powered by AMS MathViewer

- by Ivan Marin and Götz Pfeiffer PDF
- Math. Comp.
**86**(2017), 2005-2023 Request permission

## Abstract:

We prove the freeness conjecture of Broué, Malle and Rouquier for the Hecke algebras associated to the primitive complex 2-reflection groups with a single conjugacy class of reflections.## References

- Etsuko Bannai,
*Fundamental groups of the spaces of regular orbits of the finite unitary reflection groups of dimension $2$*, J. Math. Soc. Japan**28**(1976), no. 3, 447–454. MR**407199**, DOI 10.2969/jmsj/02830447 - David Bessis,
*Finite complex reflection arrangements are $K(\pi ,1)$*, Ann. of Math. (2)**181**(2015), no. 3, 809–904. MR**3296817**, DOI 10.4007/annals.2015.181.3.1 - David Bessis and Jean Michel,
*Explicit presentations for exceptional braid groups*, Experiment. Math.**13**(2004), no. 3, 257–266. MR**2103323** - Michel Broué, Gunter Malle, and Raphaël Rouquier,
*Complex reflection groups, braid groups, Hecke algebras*, J. Reine Angew. Math.**500**(1998), 127–190. MR**1637497** - E. Chavli,
*The Broué-Malle-Rouquier conjecture for reflection groups of rank $2$*, Thèse de doctorat, Université Paris-Diderot, 2016, arXiv:1608.00834. - François Digne, Ivan Marin, and Jean Michel,
*The center of pure complex braid groups*, J. Algebra**347**(2011), 206–213. MR**2846406**, DOI 10.1016/j.jalgebra.2011.06.034 - Pavel Etingof and Eric Rains,
*Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups*, J. Algebra**299**(2006), no. 2, 570–588. MR**2228327**, DOI 10.1016/j.jalgebra.2006.01.005 - Meinolf Geck and Götz Pfeiffer,
*Characters of finite Coxeter groups and Iwahori-Hecke algebras*, London Mathematical Society Monographs. New Series, vol. 21, The Clarendon Press, Oxford University Press, New York, 2000. MR**1778802** - Ivan Losev,
*Finite-dimensional quotients of Hecke algebras*, Algebra Number Theory**9**(2015), no. 2, 493–502. MR**3320850**, DOI 10.2140/ant.2015.9.493 - Ivan Marin,
*The cubic Hecke algebra on at most 5 strands*, J. Pure Appl. Algebra**216**(2012), no. 12, 2754–2782. MR**2943756**, DOI 10.1016/j.jpaa.2012.04.013 - Ivan Marin,
*The freeness conjecture for Hecke algebras of complex reflection groups, and the case of the Hessian group $G_{26}$*, J. Pure Appl. Algebra**218**(2014), no. 4, 704–720. MR**3133700**, DOI 10.1016/j.jpaa.2013.08.009 - Jean Michel,
*The development version of the CHEVIE package of GAP3*, J. Algebra**435**(2015), 308–336. MR**3343221**, DOI 10.1016/j.jalgebra.2015.03.031 - M. Picantin,
*Petits Groupes Gaussiens*, Thèse de doctorat, Université de Caen, 2000.

## Additional Information

**Ivan Marin**- Affiliation: LAMFA, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens, France
- MR Author ID: 664485
- Email: ivan.marin@u-picardie.fr
**Götz Pfeiffer**- Affiliation: School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
- Email: goetz.pfeiffer@nuigalway.ie
- Received by editor(s): September 17, 2015
- Received by editor(s) in revised form: January 12, 2016
- Published electronically: October 12, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp.
**86**(2017), 2005-2023 - MSC (2010): Primary 20C08; Secondary 20F55
- DOI: https://doi.org/10.1090/mcom/3142
- MathSciNet review: 3626546