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## Modules which are direct sum of weight spaces.

For a semisimple Lie algebra $\mathfrak{g}$, a highest weight module $V(\lambda)$ with highest weight weight $\lambda$ has the property that every submodule $W$ of $V(\lambda)$ is a direct sum of the weight spaces of $W$.

Now consider quantum affine algebra $U_q(\hat{\mathfrak{g}})$. Let $V(\lambda)$ be the highest weight $U_q(\hat{\mathfrak{g}})$-module with highest weight weight $\lambda$. Do we still have the property that every submodule $W$ of $V(\lambda)$ is a direct sum of the weight spaces of $W$?

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