Chreif, M., Abdulrahim, M. (2016). On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7. Journal of Linear and Topological Algebra (JLTA), 05(04), 263-270.

M. Y Chreif; M Abdulrahim. "On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7". Journal of Linear and Topological Algebra (JLTA), 05, 04, 2016, 263-270.

Chreif, M., Abdulrahim, M. (2016). 'On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7', Journal of Linear and Topological Algebra (JLTA), 05(04), pp. 263-270.

Chreif, M., Abdulrahim, M. On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7. Journal of Linear and Topological Algebra (JLTA), 2016; 05(04): 263-270.

On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex re ection group G7

^{1}Department of Matehmatics Faculty of Science Beirut Arab University Beirut, Lebanon P.O. Box: 11-5020

^{2}Professor Department of Mathematics Faculty of Science Beirut Arab University P.O. Box: 11-5020 Beirut, Lebanon

Abstract

We consider a 2-dimensional representation of the Hecke algebra H(G7; u), where G7 is the complex re ection group and u is the set of indeterminates u = (x1; x2; y1; y2; y3; z1; z2; z3): After specializing the indetrminates to non zero complex numbers, we then determine a nec- essary and sucient condition that guarantees the irreducibility of the complex specialization of the representation of the Hecke algebra H(G7; u).

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