$N \leftrightarrow -N$ duality of SU(N) for stable sequences of representations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913942435004416 |
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| author | Mkrtchyan, R. L. |
| author_facet | Mkrtchyan, R. L. |
| contents | We generalize $N \leftrightarrow -N$ duality of dimension formulae of $SU(N)$ representations on a (class of) representations with $N$-dependent Young diagrams (which include the adjoint representation), and on eigenvalues of the Casimir operator for those representations. We discuss the consequences for the hypothesis of universal decomposition of powers of the adjoint representation into Casimir subspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $N \leftrightarrow -N$ duality of SU(N) for stable sequences of representations Mkrtchyan, R. L. Mathematical Physics High Energy Physics - Theory 17B10, 17B25 We generalize $N \leftrightarrow -N$ duality of dimension formulae of $SU(N)$ representations on a (class of) representations with $N$-dependent Young diagrams (which include the adjoint representation), and on eigenvalues of the Casimir operator for those representations. We discuss the consequences for the hypothesis of universal decomposition of powers of the adjoint representation into Casimir subspaces. |
| title | $N \leftrightarrow -N$ duality of SU(N) for stable sequences of representations |
| topic | Mathematical Physics High Energy Physics - Theory 17B10, 17B25 |
| url | https://arxiv.org/abs/2507.10371 |