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{
    "pk": 64895,
    "title": "Highest weight crystals for Schur \\(Q\\)-functions",
    "subtitle": null,
    "abstract": "Work of Grantcharov et al. develops a theory of abstract crystals for the queer Lie superalgebra \\(\\mathfrak{q}_n\\). Such \\(\\mathfrak{q}_n\\)-crystals form a monoidal category in which the connected normal objects have unique highest weight elements and characters that are Schur \\(P\\)-polynomials. This article studies a modified form of this category, whose connected normal objects again have unique highest weight elements but now possess characters that are Schur \\(Q\\)-polynomials. The crystals in this category have some interesting features not present for ordinary \\(\\mathfrak{q}_n\\)-crystals. For example, there is an extra crystal operator, a different tensor product, and an action of the hyperoctahedral group exchanging highest and lowest weight elements. There are natural examples of \\(\\mathfrak{q}_n\\)-crystal structures on certain families of shifted tableaux and factorized reduced words. We describe extended forms of these structures that give similar examples in our new category.\n \nMathematics Subject Classifications: 05E05, 05E10\n \nKeywords: Crystals, Schur \\(Q\\)-functions, queer Lie superalgebras, shifted tableaux, involution words",
    "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": "Crystals"
        },
        {
            "word": "Schur \\(Q\\)-functions"
        },
        {
            "word": "queer Lie superalgebras"
        },
        {
            "word": "shifted tableaux"
        },
        {
            "word": "involution words"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/8hb775tk",
    "frozenauthors": [
        {
            "first_name": "Eric",
            "middle_name": "",
            "last_name": "Marberg",
            "name_suffix": "",
            "institution": "Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong",
            "department": ""
        },
        {
            "first_name": "Kam",
            "middle_name": "Hung",
            "last_name": "Tong",
            "name_suffix": "",
            "institution": "Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-14T07:20:46Z",
    "date_accepted": "2023-09-14T07:20:46Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64895/galley/49705/download/"
        }
    ]
}