Decompose the character of a $U_{q}(\mathfrak{g})$-module $M$ into a sum of characters of its irreducible submodules. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T23:01:49Z http://mathoverflow.net/feeds/question/73588 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/73588/decompose-the-character-of-a-u-q-mathfrakg-module-m-into-a-sum-of-chara Decompose the character of a $U_{q}(\mathfrak{g})$-module $M$ into a sum of characters of its irreducible submodules. Jianrong Li 2011-08-24T17:02:46Z 2011-08-24T17:02:46Z <p>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.</p>