A Characterization of SU(3) from Low-Dimensional Representation Constraints
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| Format: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901534354178048 |
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| author | Odam |
| author_facet | Odam |
| contents | <p>We prove a classification-level result for compact connected Lie groups acting on C³. Under three independently motivated assumptions — a determinant constraint, the presence of a cyclic 3-symmetry, and non-self-conjugacy of the representation — the only compact connected Lie group admitting a faithful irreducible unitary representation on C³ is SU(3). The non-self-conjugacy assumption is motivated via an Information Preservation Principle (IPP). The proof proceeds via the Peter–Weyl structure theorem, the Weyl dimension formula, and a center-quotient argument. A minimality corollary establishes that no proper compact connected subgroup of SU(3) satisfies all three conditions simultaneously.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20221773 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Characterization of SU(3) from Low-Dimensional Representation Constraints Odam <p>We prove a classification-level result for compact connected Lie groups acting on C³. Under three independently motivated assumptions — a determinant constraint, the presence of a cyclic 3-symmetry, and non-self-conjugacy of the representation — the only compact connected Lie group admitting a faithful irreducible unitary representation on C³ is SU(3). The non-self-conjugacy assumption is motivated via an Information Preservation Principle (IPP). The proof proceeds via the Peter–Weyl structure theorem, the Weyl dimension formula, and a center-quotient argument. A minimality corollary establishes that no proper compact connected subgroup of SU(3) satisfies all three conditions simultaneously.</p> |
| title | A Characterization of SU(3) from Low-Dimensional Representation Constraints |
| url | https://doi.org/10.5281/zenodo.20221773 |