Let V be the 7-dimensional irreducible representation of the quantum group Uq (g2). For each n, there is a map from the braid group Bn to the endomorphism algebra of the n-th tensor power of V, given by R matrices. Extending linearly to the braid group algebra, we get a map. Lehrer and Zhang have proved that map is surjective, as a special case of a more general result. Using Kuperberg's spider for G2, we give an elementary diagrammatic proof of this result.
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