Some rings of differential operators for \(\text{Sl}_ 2\)-invariants are simple
Let \(A\) be a finitely generated \(\mathbb{C}\)-algebra and \(G\) a reductive group acting on \(X=\text{Spec }A\). Assume that \(X\) is smooth and connected. Then it is conjectured that the ring of differential operators of the invariant ring \(A^G\) is a simple ring. In this paper some new tools are introduced which are useful to prove this conjecture in some special cases. In particular it is proved if \(G=\text{SL}_2\) and \(X\) is a reducible \(G\)-module \(M\) such that each irreducible component of the representation \(M\) has even dimension.
rings of differential operators of invariant rings
scientific article; zbMATH DE number 908496
scientific article