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.



Reference request: representation of type G2 Lie algebras.
This paper constructs the representations of $G\_2$ explicitly in terms of the Schur functor construction and multilinear operations: <http://www.ams.org/journals/proc/1999-127-03/S0002-9939-99-04583-9/home.html>


It doesn't give you a preferred basis in terms of tableaux though. For that, you might want to look at the book "Standard monomial theory" by Lakshmibai and Raghavan. But this is much less explicit. This paper of Littelmann does in much greater generality: <http://www.ams.org/jams/1998-11-03/S0894-0347-98-00268-9/S0894-0347-98-00268-9.pdf>


