The split $5$-Casimir operator and the structure of $\wedge \mathfrak{ad}^{\otimes 5}$
- Authors: Isaev A.P.1,2, Krivonos S.O.1,3
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Affiliations:
- Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow Region
- Lomonosov Moscow State University, Faculty of Physics
- Tomsk State University of Control Systems and Radioelectronics
- Issue: Vol 89, No 1 (2025)
- Pages: 18-29
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/303935
- DOI: https://doi.org/10.4213/im9594
- ID: 303935
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Abstract
In the present paper, using the split Casimir operators,we find the decomposition of the antisymmetric part ofthe fifth power of the adjoint representation$\mathfrak{ad}^{\otimes 5}$. This decomposition contains, in addition to the representations that appearesin the decomposition of $\mathfrak{ad}^{\otimes 4}$, only one newrepresentation of $X_5$. The universal dimension of this representationfor exceptional Lie algebras was proposed in [1].Our decomposition holds for all Lie algebras.
About the authors
Aleksei Petrovich Isaev
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow Region; Lomonosov Moscow State University, Faculty of Physics
Email: isaevap@theor.jinr.ru
Doctor of physico-mathematical sciences, Professor
Sergei Olegovich Krivonos
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna, Moscow Region; Tomsk State University of Control Systems and Radioelectronics
Author for correspondence.
Email: isaevap@theor.jinr.ru
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