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Denote the falling factorials by $(x)_k=x(x-1)\cdots(x-k+1)$. The Vandermonde determinant is given by $\det\left[x_i^{j-1}\right]_1^n=\prod_{i<j}(x_j-x_i)$. It is well-known that in as much as ...

Assume that you are explicitly given the representation matrices of a group. How does one go about finding that common basis which will find the irreducible components of all of them simultaneously? ...