Let $k$ be an algebraically closed field of zero characteristic, and $A_n=k\langle x_1, \ldots, x_n, \partial_1, \ldots, \partial_n \rangle$ the rank n Weyl algebra, which can also be described as a ring of differential operators: $A_n=\mathcal{D}(k^n)$.
As such, any finite subgroup $G$ of $\operatorname{GL}_n$ acts on the Weyl algebra by algebra automorphisms. A rather impressive result due to Stafford and Levasseur is that there is a very nice minimal set of algebra generators for $A_n^G$: it is generated by $k[x_1,\ldots,x_n]^G$ and $k[\partial_1,\ldots,\partial_n]^G$.
So finding generators is essentially a problem of classical invariant theory. However, if we are interested in generators and relations between them, as far as I know, this later result is not very useful: we don't have much information about the relations between this set of generators.
What is the best algorithimc approach we have to find generators and relations for invariants of the weyl algebra under the action of a finite group?
I know some results of WN Traves about this, but I don't have any other source.
