Maffei's action and symplectic Springer action for quiver varieties

We examine the relationship between the actions of two Weyl groups on the cohomology of a smooth quiver variety: the Maffei's action of the Weyl group associated to the quiver, and the symplectic Springer action of the Namikawa-Weyl group of the affine quiver variety. We show there is a natural map from the former group to the latter, which is an embedding in favorable situations, and this map intertwines their actions on the cohomology. This answers a question raised in arXiv:1904.10497.