Irreducible representations for the $A$-series Lie algebras are labelled Young diagrams, with a basis of each given by Young tableaux. Moreover, analogues exist for the $B,C$, and $D$ series.


Does such a description exist for the exceptional Lie algebras 
$$
\frak{g}\_2 \subseteq \frak{f\_4} \subseteq\frak{e}\_6 \subseteq\frak{e}\_7 \subseteq\frak{e}\_8?
$$



Young tableaux for exceptional Lie algebras
Young diagrams for the exceptional Lie algebras are considered in the book <https://press.princeton.edu/titles/8839.html> (Group Theory: Birdtracks, Lie's, and Exceptional Groups, by Predrag Cvitanovic).


