On the second cohomology groups of exceptional Lie algebras in positive characteristic

The second cohomology groups of exceptional Lie algebras $E_n$ ($n=6,7,8$), $F_4$, $G_2$ over an algebraically closed field of characteristic $p\ge h+5$ with coefficients in modules, dual to Weyl modules, are explicitly described. Here $h$ is the Coxeter number.