I'm referring to the dual group in the context of the Petery-Weyl theorem from harmonic analysis, which applies to any compact group. The dual group consists of irreducible homomorphisms from the group to the space of unitary operators. And by matrix representations, I mean defining the elements of a group as matricies in such a way that group multiplication can be computed as matrix multiplication. In SymPy and GAP groups are represented in the form of a set of permutations, with group multiplication being permutation multiplication, I think using matrix representations might be more useful, as many Lie groups (like the Heisenberg group) are defined in this way.
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