Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-0201050420161201On the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$263270525145ENM. Y.ChreifDepartment of Mathematics, Beirut Arab University,
PO. Box 11-5020, Beirut, LebanonM.AbdulrahimDepartment of Mathematics, Beirut Arab University,
PO. Box 11-5020, Beirut, LebanonJournal Article20160728We 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 specialization of the representation of the Hecke algebra $H(G_7, u)$.http://jlta.iauctb.ac.ir/article_525145_c823f0b9a87e816b0e0d7866259cf663.pdf