Some rings of differential operators for Sl2-invariants are simple

Abstract

Abstract It has been conjectured that the ring of differential operators of the algebraic quotient of a connected smooth affine variety under a reductive group action is simple. This is known in the case that the group in question is the extension of a finite group with a torus and in the case of classical representation of classical groups. In this note we present some tools relevant to this conjecture. In particular, we show that it is true for some representations of Sl2.