Tangent space of a moduli space.

Question

Let $X$ be a compact Riemann surface with genus $2$ and $M^2$ the moduli space of stable principal $SL(2)$-bundles of rank $r$. We know that $M^2$ is a complex projective variety of dimention $r^2(g-1)+1=r^2+1$. I have to prove that if $p \in M^2$ is a smooth point then $T_pM^2 \simeq H^1(X,\mathfrak{sl}(2))$. With $\mathfrak{sl}(2)$ we mean the adjoint bundle. I suppose that $H^1(X,\mathfrak{sl}(2))$ is the sheaf cohomology with coefficients the holomorphic sections of $\mathfrak{sl}(2)$ and they can be regarded as an infinite dimentional Lie algebra. How can I prove the isomorphism $T_pM^2 \simeq H^1(X,\mathfrak{sl}(2))$?