On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$

Subject Areas : History and biography

M. Y. Chreif ¹ , M. Abdulrahim ²

1 - Department of Mathematics, Beirut Arab University, PO. Box 11-5020, Beirut, Lebanon
2 - Department of Mathematics, Beirut Arab University, PO. Box 11-5020, Beirut, Lebanon

Received: 2016-07-28 Accepted : 2016-10-25 Published : 2016-12-01

Keywords:

References:

[1] D. Bessis, J. Michel, Explicit presentations for exceptional braid groups. Experiment. Math. 13 (3) (2004), 257-266.

[2] J. Birman, Braids, Links and Mapping Class Groups. Annals of Mathematical Studies, Princeton University Press, 82 (1975).

[3] M. Broue, G. Malle, R. Rouquier, Complex reflection groups, braid groups, Hecke algebras. J. reine angew. Math. 500 (1998), 127-190.

[4] M. Chlouveraki, Degree and Valuation of the Schur elements of cyclotomic Hecke algebras J. Algebra, 320 (11) (2008), 3935-3949.

[5] A. Cohen, Finite complex re ection groups. Ann. Sci. Ecole Norm. Sup. (4), 9 (3) (1976), 379-436.

[6] I. Gordon, S. Grieth, Catalan numbers for complex reflection groups. Amer. J. Math., 134 (6) (2012), 1491-1502.

[7] G. Malle, J. Michel, Constructing representations of Hecke algebras for complex reflection groups. LMS J. Comput. Math., 13 (2010), 426-450.

[8] G. Shephard, J. Todd, Finite unitary reflection groups. Canadian J. Math. 6 (1954), 274-304.