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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.13062 |
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Table of Contents:
- We consider eigenvalues of the Casimir operator on the naturally defined \textit{stable sequences} of representations of $su(N)$ algebra and prove that eigenvalues are linear over $N$ iff $λ_1+2λ_2+...+kλ_k=λ_{N-1}+2λ_{N-2}+...+kλ_{N-k}$, where $λ_i$ are Dynkin labels, and $λ_i=0$ for $k<i<N-k$, with fixed $k$. These representations are exactly those which appear in the decomposition of $ad(su(N))^{\otimes k}$, therefore this linearity admits the presentation of eigenvalues in the universal, in Vogel's sense, form, and supports the hypothesis of universal decomposition of $ad^{\otimes k}$ into Casimir eigenspaces.