Affine $G_2$ Centralizer Algebras

Abstract: We show that $${\rm End}<em>{\bf U}(V</em>\lambda\otimes V^{\otimes n})$$ 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 $V_\lambda$ is an arbitrary irreducible representation.