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: Braid group, Hecke algebra, irreducible, reflections,

Abstract :

We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where$G_7$ is the complex reflection group and $u$ is the set of indeterminates$u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$.After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specializationof the representation of the Hecke algebra $H(G_7, u)$.

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