Is there a way with GAP to get the tensor product of representations in a certain basis?
To be more specific, I would like to cross-check with GAP the tensor products of, for example A5, as given in equations (82)-(86) in https://arxiv.org/abs/1003.3552
I give here eq.(82), so you don't need to open the paper itself to see an example of what I'm looking for.
\begin{eqnarray} \left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \\ \end{array} \right)_{{\bf 3}} \otimes \left( \begin{array}{c} y_1 \\ y_2 \\ y_3 \\ \end{array} \right)_{{\bf 3}} &=& (x_1y_1+x_2y_2+x_3y_3)_{{\bf 1}} \oplus \left( \begin{array}{c} x_3y_2 - x_2y_3 \\ x_1y_3-x_3y_1 \\ x_2y_1-x_1y_2 \\ \end{array} \right)_{{\bf 3}} \nonumber\\ & \oplus & \left( \begin{array}{c} x_2y_2 - x_1y_1 \\ x_2y_1+x_1y_2 \\ x_3y_2+x_2y_3 \\ x_1y_3+x_3y_1 \\ -\frac{1}{\sqrt3}(x_1y_1+x_2y_2-2x_3y_3) \end{array} \right)_{{\bf 5}}, \end{eqnarray}
For A5 I can do it fairly easy by hand, but for larger groups it would be nice to cross-check with GAP or something else.