let $T=T_{a,u}(v)$ be transvection, I want to find centralizer of $T_{a,u}(v)$ in $GL(V)$. What is $C _{GL(V)}(T)$?
$T_{a,u}(v)=v+u(v)a$ where $a$ is vector in vector space $V$ on field $F$ and $u$ is linear functional on $V$.It is not hard to see $T_{a,u}(v)\in SL(V)$
I have not any idea how to deal with it.