In this note, we study formal deformations of derived representations of the principal series representations of $\mathrm{SL}(2,ℝ)$. In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for $\mathrm{SL}(2,ℂ)$.

Let $M$ be a differential manifold. Let $\Phi$ be a Drinfeld associator. In this paper we explain how to construct a global formality morphism starting from $\Phi$. More precisely, following Tamarkin’s proof, we construct a Lie homomorphism “up to homotopy" between the Lie algebra of Hochschild cochains on $C^{\infty }\left(M\right)$ and its cohomology $(\Gamma (M,\Lambda TM),{[-,-]}_S$). This paper is an extended version of a course given 8 - 12 March 2004 on Tamarkin’s works. The reader will find explicit examples, recollections on $G_{\infty }$-structures, explanation of the...