{
  "abstract": "Applying some simple rules, established in group theory literature, generated are codes (easy to modify as required) for obtaining $SU(3)$ irreducible representations (irreps) for a given number of nucleons in a given oscillator shell $η$ with $η\\le 8$. In this approach, first the $SU(3)$ irreps are obtained for spinless fermions in a given $η$ shell. Using the codes developed, tables of $SU(3)$ irreps are generated for identical nucleons (protons or neutrons) with a given total spin $S$. Similarly, the $SU(3)$ irreps are generated for nucleons with a given spin-isospin $SU(4)$ irrep. Some applications of these tables for $η=4$ shell for $52 \\le \\mbox{Z,N} \\le 78$ nuclei with proxy-$SU(4)$ symmetry are presented. Also, the procedure used for the shell model $SU(3)$ limits is easy to be extended for the $SU(3)$ limit of various interacting boson models and some examples for these are also presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39357",
  "author_total": 1,
  "authors": [
    {
      "name": "V. K. B. Kota"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekaqsjrb1x4h7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39357",
  "fulltext_url": null,
  "id": "ekaqsjrb1x4h7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39357",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nucl-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39357",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekaqsjrb1x4h7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39357",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39357"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    }
  ],
  "title": "Irreducible representations of $SU(3)$ for nucleons in a oscillator shell $η$ with $η\\le 8$: Application to nuclei with proxy-$SU(4)$ symmetry",
  "title_text": "Irreducible representations of SU(3) for nucleons in a oscillator shell η with η≤ 8: Application to nuclei with proxy-SU(4) symmetry",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ekaqsjrb1x4h7",
  "venue": "arXiv",
  "versions": []
}