Linear maps preserving invariants

Details Linear maps preserving invariants Linear maps preserving invariants

2007-08-21

arxiv.org/abs/0708.2890v3

Mathematics

Representation Theory

minor changes

Scientific paper

Let $G\subset\GL(V)$ be a complex reductive group. Let $G'$ denote
$\{\phi\in\GL(V)\mid p\circ\phi=p\text{for all} p\in\C[V]^G\}$. We show that,
in general, $G'=G$. In case $G$ is the adjoint group of a simple Lie algebra
$\lieg$, we show that $G'$ is an order 2 extension of $G$. We also calculate
$G'$ for all representations of $\SL_2$.

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