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{
    "pk": 65038,
    "title": "Growth diagram proofs for the Littlewood identities",
    "subtitle": null,
    "abstract": "The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be \"bijectivised\" to obtain RSK like correspondences. In this paper we give a concise overview of this machinery and extend it to Littlewood type identities by introducing a new family of relations between these operators, called projection identities. Thereby we obtain infinite families of bijections for the Littlewood identities generalising the classical ones. We believe that this approach will be useful for finding bijective proofs for Littlewood type identities in other settings such as for Macdonald polynomials and their specialisations, alternating sign matrices or vertex models.\n \nMathematics Subject Classifications: 05E05, 05A19\n \nKeywords: Littlewood identity, growth diagrams, Robinson-Schensted-Knuth correspondence, RSK, Schur polynomials",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Littlewood identity"
        },
        {
            "word": "growth diagrams"
        },
        {
            "word": "Robinson-Schensted-Knuth correspondence"
        },
        {
            "word": "RSK"
        },
        {
            "word": "Schur polynomials"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9q35h859",
    "frozenauthors": [
        {
            "first_name": "Florian",
            "middle_name": "",
            "last_name": "Schreier-Aigner",
            "name_suffix": "",
            "institution": "Faculty of Mathematics, University of Vienna, Vienna, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T22:23:50+03:00",
    "date_accepted": "2026-04-20T22:23:50+03:00",
    "date_published": "2026-04-20T10:00:00+03:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65038/galley/49848/download/"
        }
    ]
}