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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2311.05358 |
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| _version_ | 1866911786017488896 |
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| author | Avetisyan, Maneh Isaev, Alexey Krivonos, Sergey Mkrtchyan, Ruben |
| author_facet | Avetisyan, Maneh Isaev, Alexey Krivonos, Sergey Mkrtchyan, Ruben |
| contents | We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation $\mathfrak{g}^{\otimes 4}$ for all simple Lie algebras. We present universal, in Vogel's sense, formulae for the dimensions and split Casimir operator's eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulae exists for an arbitrary power of the adjoint representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05358 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The uniform structure of $\mathfrak{g}^{\otimes 4}$ Avetisyan, Maneh Isaev, Alexey Krivonos, Sergey Mkrtchyan, Ruben Mathematical Physics High Energy Physics - Theory We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation $\mathfrak{g}^{\otimes 4}$ for all simple Lie algebras. We present universal, in Vogel's sense, formulae for the dimensions and split Casimir operator's eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulae exists for an arbitrary power of the adjoint representations. |
| title | The uniform structure of $\mathfrak{g}^{\otimes 4}$ |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.05358 |