| B型和C型Weyl模的一个新重数公式 |
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| 引用本文： | 叶家琛,云本胜,詹佳. B型和C型Weyl模的一个新重数公式[J]. 数学研究及应用, 2010, 30(4): 675-686. DOI: 10.3770/j.issn:1000-341X.2010.04.012 |
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| 作者姓名： | 叶家琛 云本胜 詹佳 |
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| 作者单位： | 同济大学数学系, 上海 200092;同济大学数学系, 上海 200092;同济大学数学系, 上海 200092 |
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| 基金项目： | 国家自然科学基金(No.10671142). |
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| 摘 要： | A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(gl) of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V (λ) as a U(gl)-module into a direct sum of Weyl modules V (μ)’s as U(gl-1)modules is described. In particular, a new multiplicity formula for the Weyl module V (λ) is obtained in this note.
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| 关 键 词： | simple Lie algebra multiplicity formula weight irreducible module. |
| 收稿时间： | 2008-06-26 |
| 修稿时间： | 2008-12-18 |
A New Multiplicity Formula for the Weyl Modules of Type $B$ and $C$ |
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| Jia Chen YE,Ben Sheng YUN and Jia ZHAN. A New Multiplicity Formula for the Weyl Modules of Type $B$ and $C$[J]. Journal of Mathematical Research with Applications, 2010, 30(4): 675-686. DOI: 10.3770/j.issn:1000-341X.2010.04.012 |
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| Authors: | Jia Chen YE Ben Sheng YUN Jia ZHAN |
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| Affiliation: | Department of Mathematics,Tongji University,Shanghai 200092,P.R.China |
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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. |
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| Keywords: | simple Lie algebra multiplicity formula weight irreducible module. |
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