A homomorphism of Harish-Chandra and direct images of \(\mathcal{D}\)-modules (Q2750841)

Let \(\mathfrak{g}\) be a complex semisimple Lie algebra with adjoint group \(G\), Cartan subalgebra \(\mathfrak{h}\) and Weyl group \(W\). There is a celebrated homomorphism \(\delta:D(\mathfrak{g})^{G}\rightarrow D(\mathfrak{h})^{W}\), defined by Harish-Chandra, of algebras of invariant polynomial differential operators. The authors show that this homomorphism naturally arises in the context of \(D\)-modules.