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I make this question because I'd like to have an explicit example of moduli space. First of all, we consider $G=SL(2,\mathbb{C})$ and $X$ a compact Riemann surface with genus $2$. So we can build $M^2$: the moduli space of principal stable $SL(2)$-bundles on $X$. In order to do this, I cite this answer http://math.stackexchange.com/questions/518746/principal-stable-sl2-bundles-on-a-genus-2-compact-riemann-surface, in order to have a model of principal $SL(2)$-bundle on $X$. Now, how can I build ''with hands'' the moduli space $M^2$?

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