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We define a semisimple $U'_q({\\mf g})$-module structure on $\\E^{\\otimes 2}$ in terms of q-deformed Clifford generators, where $\\E$ is the exterior algebra generated by a dual natural representation $V$ of $U_q(\\mf{sl}_{n})$. We show that each $W(\\varpi_k)$ appears as an irreducible summand (not necessarily multiplicity free) in $\\E^{\\otimes 2}$. 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