In 2010, Namikawa famously showed that the Poisson deformations of a conic symplectic singularity can be classified by a “universal Poisson deformation”, a large Poisson scheme over a base, from which every other Poisson deformation can be obtained by base change. This was initially expressed (and proven) by showing that the Poisson deformation functor is representable. More recently Losev showed that this universal deformation can be quantized and that this quantization enjoys a universal property with nice compatibility. Together with Ambrosio, Carnovale, Esposito we expressed Losev’s theorem in terms of the representability of a functor of quantizations of Poisson deformations. This formal language leads to an easy proof of the existence and uniqueness of universal equivariant deformations and quantizations with respect to a group of C*-Poisson symmetries. I will describe a few applications of this work to the equivariant deformation theory of nilpotent Slodowy varieties, a class of symplectic singularities obtained from nilpotent cones by Hamiltonian reduction.

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