论文标题
关于Burau和Gassner代表的扩展的不可约性
On the irreducibility of the extensions of Burau and Gassner representations
论文作者
论文摘要
我们研究$ cb_ {n} $的$ n $ th度表示$ \ hat {ρ_g} $和$ c_ {n} $的$ \ hat {ρ_b} $，由Valerij G. bardakov定义，由$ cb_ {n} $ conjug is conjug is conjugs and usomormorphismss of conjugs和conjugs的组合自动形态。我们证明$ \ hat {ρ_g} $是可还原的，其$（n-1）$（n-1）$ th度组成因子$ \ hat {ϕ_g} $仅当$ t_i \ neq 1 $ for ALL $ 1 \ leq i \ leq i \ leq n $时，仅当$ t_i \ neq 1 $时。另外，我们证明$ \ hat {ρ_b} $是可还原的，其$（n-1）$（n-1）$ th度组成因子$ \ hat {ϕ_b} $在且仅当$ t \ neq 1 $时才不可修复。此外，对于$ n = 3 $，我们证明$ \ hat {ϕ_g}（t_1，t_1，t_2，t_3）\ otimes \ hat \ hat {ϕ_g}（m_1，m_2，m_3，m_3）$在且仅当$（t_1，t_1，t_2，t_2，t_3）$和$ __________和m__1，m_2，m_2，m_2，m_3）$是不可修复的表示$ \ hat {ϕ_b}（t）\ otimes \ hat {ϕ_b}（m）$在且仅当$ t \ neq m $时才不可修复。
We study the $n$th degree representations $\hat{ρ_G}$ of $Cb_{n}$ and $\hat{ρ_B}$ of $C_{n}$, defined by Valerij G. Bardakov, where $Cb_{n}$ is the group of basis conjugating automorphisms and $C_n$ is the group of conjugating automorphisms. We prove that $\hat{ρ_G}$ is reducible and its $(n-1)$th degree composition factor $\hat{ϕ_G}$ is irreducible if and only if $t_i\neq 1$ for all $1\leq i \leq n$. Also we prove that $\hat{ρ_B}$ is reducible and its $(n-1)$th degree composition factor $\hat{ϕ_B}$ is irreducible if and only if $t\neq 1$. Moreover, for $n=3$, we prove that $\hat{ϕ_G}(t_1,t_2,t_3) \otimes \hat{ϕ_G}(m_1,m_2,m_3)$ is irreducible if and only if $(t_1,t_2,t_3)$ and $(m_1,m_2,m_3)$ are distinct vectors, and the representation $\hat{ϕ_B}(t) \otimes \hat{ϕ_B}(m)$ is irreducible if and only if $t \neq m$.
