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{
    "pk": 64831,
    "title": "Intersecting principal Bruhat ideals and grades of simple modules",
    "subtitle": null,
    "abstract": "We prove that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's $\\mathbf{a}$-function. Our arguments are combinatorial, and include a description of the intersection of two principal order ideals when at least one permutation is boolean. An important object in our work is a reduced word written as minimally many runs of consecutive integers, and one step of our argument shows that this minimal quantity is equal to the length of the second row in the permutation's shape under the Robinson-Schensted correspondence. We also prove that a simple module over the above-mentioned incidence algebra is perfect if and only if its index is the longest element of a parabolic subgroup.\n \nMathematics Subject Classifications: 20F55, 06A07, 05E15",
    "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": "Incidence algebra"
        },
        {
            "word": "grade"
        },
        {
            "word": "boolean permutation"
        },
        {
            "word": "a-function"
        },
        {
            "word": "principal ideal"
        },
        {
            "word": "symmetric group"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/35x678r9",
    "frozenauthors": [
        {
            "first_name": "Volodymyr",
            "middle_name": "",
            "last_name": "Mazorchuk",
            "name_suffix": "",
            "institution": "Department of Mathematics, Uppsala University, Uppsala, Sweden",
            "department": ""
        },
        {
            "first_name": "Bridget",
            "middle_name": "Eileen",
            "last_name": "Tenner",
            "name_suffix": "",
            "institution": "Department of Mathematical Sciences, DePaul University, Chicago, IL, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T20:44:11Z",
    "date_accepted": "2022-03-23T20:44:11Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64831/galley/49641/download/"
        }
    ]
}