Publications

Let $Cb_n$ be the group of basis conjugating automorphisms of a free group $\mathbb{F}_n$, and $C_n$ the group of conjugating automorphisms of $\mathbb{F}_n$. Valerij G. Bardakov has constructed representations of $Cb_n$, $C_n$ in the groups $GL_n(\mathbb{Z}[{t_1}^{\pm1}, \ldots ,{t_n}^{\pm 1}])$ and in $GL_n(\mathbb{Z}[{t}^{\pm1}])$ respectively, where $t_1, \ldots, t_n, t$ are indeterminate variables. We show that these representations are reducible and we determine the irreducible components of the representations in $GL_n(\mathbb{C})$, which are obtained by giving values to the variables above. Next, we consider the tensor product of the representations of $Cb_n$, $C_n$ and study their irreduciblity in the case $n=3$.