The rational non-freeness conjecture for two parabolic generators
Let Gα=⟨[1101],[10α1]⟩<SL2(C)G_{\alpha}=\left\langle \begin{bmatrix}1&1\\0&1\end{bmatrix},\begin{bmatrix}1&0\alpha&1\end{bmatrix}\right\rangle<\operatorname{SL}_2(\mathbb{C})Gα=⟨[1011],[10α1]⟩<SL2(C), and call α\alphaα free whe…