  A finite order element $g$ of a group $G$ is called rational if $g$ is
conjugate to $g^i$ for every integer $i$ coprime to the order $g$. We determine
all triples $(G,g,\phi)$, where $G$ is a simple algebraic group of type
$A_n,B_n$ or $C_n$ over an algebraically closed field of characteristic $p\geq
0$, $g\in G$ is a rational odd order semisimple element and $\phi$ is an
irreducible representation of $G$ such that $\phi(g)$ has eigenvalue 1.
