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Research Article | Open Access

Dimension formulas of the highest weight exceptional Lie algebra-modules

Yupei Zhang1, Yongzhi Luan2,3( )
College of Science, Civil Aviation University of China, Tianjin, 300300, China
Shenzhen Research Institute of Shandong University, A301 Virtual University Park in South District, Shenzhen, China
School of Mathematics, Shandong University, Jinan, 250100, China
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Abstract

Given a complex simple exceptional Lie algebra g , let V λ be an irreducible finite-dimensional g -module with highest weight λ. We provide the precise dimension formula of dim ⁡ V λ .

Keywords

Dynkin indexWeyl dimension formulaexceptional Lie algebrahighest weight modulesymbolic computation
CLC number: 17-04, 17B10, 17B25

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 10010-10030
DOI: 10.3934/math.2024490

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Cite this article:
Zhang Y, Luan Y. Dimension formulas of the highest weight exceptional Lie algebra-modules. AIMS Mathematics, 2024, 9(4): 10010-10030. https://doi.org/10.3934/math.2024490

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Received: 11 December 2023
Revised: 18 February 2024
Accepted: 26 February 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)