| A New Multiplicity Formula for the Weyl Modules of Type $B$ and $C$ |
| Received:June 26, 2008 Revised:December 18, 2008 |
| Key Words:
simple Lie algebra multiplicity formula weight irreducible module.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10671142). |
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| Abstract: |
| A monomial basis and a filtration of subalgebras for the universal enveloping algebra $\U(\g_l)$ of a complex simple Lie algebra $\frak g_l$ of type $B_l$ and $C_l$ are given, and the decomposition of the Weyl module $V(\la)$ as a $\U(\g_l)$-module into a direct sum of Weyl modules $V(\mu)$'s as $\U(\g_{l-1})$-modules is described. In particular, a new multiplicity formula for the Weyl module $V(\la)$ is obtained in this note. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.04.012 |
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