Unstable vector in a rational representation
= Unstable vector in a rational representation
{title2=$0\in\overline{Gv}$}
A vector is unstable if zero lies in the Zariski closure of its orbit. For complex $SL_n$, this is equivalent to an <algebraic one-parameter subgroup> taking it to zero as $t\to0$. In the subgroup's weight decomposition, exactly the positive-weight components can occur in such a vector.