Irreducible <inline-formula><tex-math id="M1">\begin{document}${\frak{sl}}_2$\end{document}</tex-math></inline-formula>-decomposition for a highest weight <inline-formula><tex-math id="M2">\begin{document}$\widehat{{\frak{sl}}_2}$\end{document}</tex-math></inline-formula>-module

CHAI Wei-jun; XIA Li-meng

doi:10.3969/j.issn.1000-5641.2018.03.003

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CHAI Wei-jun, XIA Li-meng. Irreducible ${\frak{sl}}_2$-decomposition for a highest weight $\widehat{{\frak{sl}}_2}$-module[J]. Journal of East China Normal University (Natural Sciences), 2018, (3): 25-29. doi: 10.3969/j.issn.1000-5641.2018.03.003

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CHAI Wei-jun, XIA Li-meng. Irreducible ${\frak{sl}}_2$-decomposition for a highest weight $\widehat{{\frak{sl}}_2}$-module[J]. Journal of East China Normal University (Natural Sciences), 2018, (3): 25-29. doi: 10.3969/j.issn.1000-5641.2018.03.003

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Irreducible ${\frak{sl}}_2$-decomposition for a highest weight $\widehat{{\frak{sl}}_2}$-module

doi: 10.3969/j.issn.1000-5641.2018.03.003

CHAI Wei-jun,
XIA Li-meng^,

Institute of Applied System Analysis, Jiangsu University, Zhenjiang Jiangsu 212013, China

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Corresponding author: 夏利猛, 男, 教授, 研究方向为李代数及其表示理论.E-mail:xialimeng@ujs.edu.cn
Received Date: 2017-03-22
Publish Date: 2018-05-25

Abstract

Abstract

In this paper, we study the irreducible highest weight module $L(\Lambda_0)$ of affine Lie algebra $\widehat{{\frak{sl}}_2}$. Since the three-dimensional simple algebra ${\frak{sl}}_2$ is regarded as a Lie subalgebra of $\widehat{{\frak{sl}}_2}$, $L(\Lambda_0)$ naturally becomes a ${{\frak{sl}}_2}$-module. We present the irreducible decomposition of $L(\Lambda_0)$ as a ${{\frak{sl}}_2}$-module.
- affine Lie algebra,
- module,
- irreducible decomposition

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References(3)

References

[1]	FRENKEL I, LEPOWSKY J, MEURMAN A. Vertex operator algebras and the monster[M]. Boston:Academic Press, 1989.
[2]	KAC V G. Infinite-dimensional Lie algebras[M]. 3rd ed. Cambridge:Cambridge University Press, 1990.
[3]	LEPOWSKY J, WILSON R. The structure of standard modules, Ⅰ:Universal algebras and the Rogers-Ramanujan identities[J]. Invent Math, 1984(77):199-290. doi: 10.1007/BF01388447