Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbb{C}$, $G$ be the corresponding simply connected algebraic group and $\mathbb{O}⊂\mathfrak{g}^∗$ be a nilpotent coadjoint orbit. In this talk I will prove that the set of $G$-equivariant formal graded quantizations of $\mathbb{O}$ is an affine space.
The key part of the proof is to construct a bijection between the sets of $G$-equivariant formal graded quantizations of $\mathbb{O}$ and its affinization $Spec(\mathbb{C}[\mathbb{O}])$. The latter set is an affine space due to a result of Losev. This talk is based on arXiv:1810.11531.