Finite dimensional representations of invariant differential operators
英文摘要：
Let $k$ be an algebraically closed field of characteristic 0, $Y=k^{r}\times {(k^{\times})}^{s}$ and let $G$ be an algebraic torus acting diagonally on the ring of differential operators $\cD (Y)^G$. We give necessary and sufficient conditions for $\cD (Y)^G$ to have enough simple finite dimensional representations, in the sense that the intersection of the kernels of all the simple finite dimensional representations is zero. As an application we show that if $K\longrightarrow GL(V)$ is a representation of a reductive group $K$ and if zero is not a weight of a maximal torus of $K$ on $V$, then $\cD (V)^K$ has enough finite dimensional representations. We also construct examples of FCR- algebras with any GK dimension $\geq 3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
