Affine $G_2$ Centralizer Algebras

We show that ${\rm End}_{\bf U}(V_λ\otimes V^{\otimes n})$ is generated by the affine braid group $AB_n$ where ${\bf U}=U_q\mathfrak g(G_2)$, $V$ is its 7-dimensional irreducible representation and $V_λ$ is an arbitrary irreducible representation.

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