Linear maps preserving invariants

Gerald W. Schwarz

Let $G\subset\GL(V)$ be a complex reductive group. Let $G^{\prime }$ denote $\{ϕ\in\GL(V)\mid p\circϕ=p\text{for all} p\in\C[V]^G\}$. We show that, in general, $G^{\prime }=G$. In case $G$ is the ad…