## Decompose the character of a $U_{q}(\mathfrak{g})$-module $M$ into a sum of characters of its irreducible submodules.

Let $\mathfrak{g}$ be a semi-simple Lie algebra and $U_{g}(\mathfrak{g})$ be the Drinfel'd-Jimbo quantum group of $\mathfrak{g}$. If we know the character of a highest weight $U_{q}(\mathfrak{g})$-module $V_{\lambda}$: $ch(V_{\lambda}) = \sum_{\mu} dim(V_{\mu})\mu$, where $V_{\mu}$'s are the weight spaces of $V_{\lambda}$. How can we decompose $ch(V_{\lambda})$ into a sum of characters of sub-modules of $V_{\lambda}$? Are there some reference? Thank you very much.

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