Holomorphic Affine Vector Fields on Weil Bundles

We obtain necessary and sufficient conditions for a holomorphic vector field to be affine for a holomorphic linear connection defined on a Weil bundle. We also prove that the Lie algebra over $\mathbb{R}$ of holomorphic affine vector fields for the natural prolongation of a linear connection from the base to the Weil bundle is isomorphic to the tensor product of the Weil algebra by the Lie algebra of affine vector fields on the base.