Dimension formulas of the highest weight exceptional Lie algebra-modules

Yupei Zhang; Yongzhi Luan; Yupei Zhang; Yongzhi Luan

doi:10.3934/math.2024490

AIMS Mathematics

2024, Volume 9, Issue 4: 10010-10030. doi: 10.3934/math.2024490

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Dimension formulas of the highest weight exceptional Lie algebra-modules

Yupei Zhang ¹,
Yongzhi Luan ^{2,3
,
,}

1.
College of Science, Civil Aviation University of China, Tianjin, 300300, China
2.
Shenzhen Research Institute of Shandong University, A301 Virtual University Park in South District, Shenzhen, China
3.
School of Mathematics, Shandong University, Jinan, 250100, China

Received: 11 December 2023 Revised: 18 February 2024 Accepted: 26 February 2024 Published: 13 March 2024
MSC : 17-04, 17B10, 17B25

Given a complex simple exceptional Lie algebra $ \mathfrak g $, let $ \mathscr V_\lambda $ be an irreducible finite-dimensional $ \mathfrak g $-module with highest weight $ \lambda $. We provide the precise dimension formula of $ \dim \mathscr V_{\lambda} $.
- Dynkin index,
- Weyl dimension formula,
- exceptional Lie algebra,
- highest weight module,
- symbolic computation
Citation: Yupei Zhang, Yongzhi Luan. Dimension formulas of the highest weight exceptional Lie algebra-modules[J]. AIMS Mathematics, 2024, 9(4): 10010-10030. doi: 10.3934/math.2024490

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Abstract

Given a complex simple exceptional Lie algebra $ \mathfrak g $, let $ \mathscr V_\lambda $ be an irreducible finite-dimensional $ \mathfrak g $-module with highest weight $ \lambda $. We provide the precise dimension formula of $ \dim \mathscr V_{\lambda} $.

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