Gerald Schwarz

"Finite dimensional representations of invariant differential operators"

Let G be a reductive complex algebraic group and V a finite dimensional G-module. Set B:=D(V)^G, the invariant algebraic differential operators on V. We consider the following general questions:

• What is the representation theory of B?
• Does B have finite dimensional representations? In particular, is B an FCR-algebra?

We answer these questions when V is the adjoint representation of SL₃.