TITLE: Reference request: representation of type G2 Lie algebras.
QUESTION [6 upvotes]: Let $\mathfrak{g}$ be an Lie algebra of type G2. Are there some combinatorial ways to describe a basis of a $\mathfrak{g}$-module? For classical types, there is a method used tableaux. Thank you very much.

REPLY [2 votes]: Another direction, that works (only?) for groups of rank at most 2, is Kuperberg's "spider" model: http://arxiv.org/abs/q-alg/9712003 .  The web diagrams he constructs generalize tableaux, in the sense that the $A_1$ and $A_2$ versions are in bijection with tableaux (at least of rectangular shape).  This is not quite the same as constructing representations via Schur functors, but it has a combinatorial appeal.