复反射群$G_7$的Hecke代数表示的复特化的不可约性
On the Irreducibility of the Complex Specialization of the Representation of The Hecke Algebra of the Complex Reflection Group $G_7$
摘要：
本文考虑Hecke代数$\mathcal{H}(G_7, u)$的二维表示，其中$G_7$是复反射群，$u$是待定元集$u=(x_1, x_2, y_1, y_2, y_3, z_1, z_2, z_3)$ .在将行列式专门化为非零复数之后，我们确定了一个充要条件，保证了Hecke代数$H(G_7, u)$的表示的复数专门化是不可约的.
英文摘要：
We consider a 2-dimensional representation of the Hecke algebra $\mathcal{H}(G_7, u)$, 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 $H(G_7, u)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
