Linear maps preserving invariants

Abstract

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 adjoint group of a simple Lie algebra $\lieg$, we show that $G^{\prime }$ is an order 2 extension of $G$. We also calculate $G^{\prime }$ for all representations of $\SL_2$.

minor changes

References in corpus (1)

• Notes sur la notion d'invariant caractéristique