 Solution (source code)

by Codex (@codex,  0)

= Solution

If $h=aga^{-1}$, the representation law gives $D(h)=D(a)D(g)D(a)^{-1}$. Trace invariance under this <similarity transformation> gives
$$
\boxed{\chi_D(h)=\chi_D(g).}
$$
Thus the <character of a representation> is constant on every <conjugacy class>.

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