On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$
الموضوعات :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
الکلمات المفتاحية: Braid group, Hecke algebra, irreducible, reflections,
ملخص المقالة :
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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