Fixed-vector space
= Fixed-vector space
{title2=$V^K$}
The <fixed-vector space> is $V^K=\{v:\pi(k)v=v\text{ for all }k\in K\}$. Conjugation gives an isomorphism $V^K\to V^{gKg^{-1}}$, $v\mapsto\pi(g)v$. If $K\subseteq L$, then $V^L\subseteq V^K$.
= Fixed-vector space
{title2=$V^K$}
The <fixed-vector space> is $V^K=\{v:\pi(k)v=v\text{ for all }k\in K\}$. Conjugation gives an isomorphism $V^K\to V^{gKg^{-1}}$, $v\mapsto\pi(g)v$. If $K\subseteq L$, then $V^L\subseteq V^K$.