= Crystal of the seven-dimensional G2 representation
The seven-dimensional irreducible representation of the <G2 root system> has <highest weight> $\omega_1=2\alpha_1+\alpha_2$. Its <crystal basis> is the chain of weights $2\alpha_1+\alpha_2,\alpha_1+\alpha_2,\alpha_1,0,-\alpha_1,-\alpha_1-\alpha_2,-2\alpha_1-\alpha_2$, with successive edge colors $1,2,1,1,2,1$. Each step subtracts its color's <simple root>. The nonzero weights are the six short roots, each of <multiplicity> one; the zero weight also has multiplicity one.
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