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

Look up the original version of Tannakian duality, stating that [math]G[/math] can be recovered from the knowledge of its full category of representations [math]\mathcal R_G[/math], viewed as subcategory of the category [math]\mathcal H[/math] of the finite dimensional Hilbert spaces, with each [math]\pi\in\mathcal R_G[/math] corresponding to its Hilbert space [math]H_\pi\in\mathcal H[/math], and write down a brief account of this.