Finite dimensional irreducible representations of Lie superalgebra D(2,1;α)

陈曦 ¹杨文力 ²丁祥茂 ³张耀中⁴

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作者信息

1. College of Intelligent Systems Science and Engineering,Hubei Minzu University 445000,China
2. Institute of Modern Physics,Northwest University,Xian 710069,China
3. Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China
4. School of Mathematics and Physics,The University of Queensland,Brisbane,QLD 4072,Australia
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Abstract

This paper focuses on the finite dimensional irreducible representations of Lie superalgebra D(2,1;α).We explicitly construct the finite dimensional representations of the superalgebra D(2,1;α)by using the shift operator and differential operator representations.Unlike ordinary Lie algebra representation,there are typical and atypical representations for most superalgebras.Therefore,its typical and atypical representation conditions are also given.Our results are expected to be useful for the construction of primary fields of the corresponding current superalgebra of D(2,1;α).

Key words

superalgebra/representations/shift operator/conformal field theory

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基金项目

国家自然科学基金(11405 051)

Australian Research Council Discovery Project(DP190101529)

国家自然科学基金(11 775 299)

出版年

2024

理论物理通讯(英文版)

中国科学院理论物理研究所中国物理学会

理论物理通讯(英文版)

CSTPCD

影响因子：0.333

ISSN：0253-6102

参考文献量32

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