[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that we have [math]S_3=S_3^+[/math] by looking at the coaction

[[math]] \Phi:\mathbb C^3\to\mathbb C^3\otimes C(S_3^+) [[/math]]

written in terms of the Fourier basis of [math]\mathbb C^3[/math].