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The induced supermodule $H^0_G(\\lambda)$, corresponding to a dominant weight $\\lambda$ of $G$, can be represented as $H^0_{G_{ev}}(\\lambda)\\otimes \\Lambda(Y)$, where $Y=V_m^*\\otimes V_n$ is a tensor product of the dual of the natural $GL(m)$-module $V_m$ and the natural $GL(n)$-module $V_n$, and $\\Lambda(Y)$ is the exterior algebra of $Y$. 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