How can I get the Wedderburn decomposition of the module $KG$, if I have the irreducible represenations of the group $G$? I am confused by a post here I found:
Why is the Wedderburn formula in this case wrong?
The last summand in the Wedderburn decomposition is $Mat(2,F_9)$, but the associated irreducible representation is $< \begin{pmatrix} \ & \ & \ & 1 \\ \ & \ & 1 & \ \\ \ & 1 & \ & \ \\ 1 & \ & \ & \ \end{pmatrix} , \begin{pmatrix} \ & 1 & \ & \ \\ \ & \ & 1 & \ \\ \ & \ & \ & 1 \\ -1 & -1 & -1 & -1 \end{pmatrix} >. $ I.E. this are matrices in $Mat(4,F_{3})$ (this is linked in the post). Why do I write than $Mat(2,F_9)$ as a summand?