Namikawa-Weyl groups of quiver varieties

Nakajima’s quiver varieties are moduli spaces of quiver representations which bear an additional symplectic structure. Out of such a symplectic singularity, Namikawa constructs a “Namikawa-Weyl group” by means of deformation theory, but implementing his construction in case of quiver varieties remains open until today. In this talk, I recapitulate how quiver varieties arise from representation theory, what is already known about Namikawa-Weyl groups of other symplectic singularities, and how Raf Bocklandt and I almost succeeded in the case of quiver varieties during my 2018 master thesis. I will highlight some remaining technical problems, which concern the difference between the algebraic and analytic world and how to construct non-affine GIT quotients.