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{
    "pk": 64986,
    "title": "Maps related to polar spaces preserving an extremal Weyl distance",
    "subtitle": null,
    "abstract": "Let \\(\\Omega_i\\) and \\(\\Omega_j\\) be the sets of elements of respective types \\(i\\) and \\(j\\) of a polar space \\(\\Delta\\) of rank at least \\(3\\). We show that a permutation \\(\\rho\\) of \\(\\Omega_i \\cup \\Omega_j\\) with the property that, for each \\(I \\in \\Omega_i \\) and \\(J\\in\\Omega_j\\), \\(I\\) and \\(J\\) generate a maximal singular subspace in \\(\\Delta\\) if and only if \\(\\rho(I)\\) and \\(\\rho(J)\\) generate a maximal singular subspace in \\(\\Delta\\), is induced by an automorphism of \\(\\Delta\\). Building-theoretically, this means that if \\(\\rho\\) preserves a certain Weyl distance in the Tits-building corresponding to \\(\\Delta\\), then it preserves all Weyl-distances.\n \nMathematics Subject Classifications: 51E24, 51A50\n \nKeywords: Polar spaces, Weyl distance",
    "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": "Polar spaces"
        },
        {
            "word": "Weyl distance"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7r35q8w5",
    "frozenauthors": [
        {
            "first_name": "Anneleen",
            "middle_name": "",
            "last_name": "De Schepper",
            "name_suffix": "",
            "institution": "Department of Mathematics, Ghent University, Ghent, Belgium",
            "department": ""
        },
        {
            "first_name": "Antonio",
            "middle_name": "",
            "last_name": "Pasini",
            "name_suffix": "",
            "institution": "Department of Information Engineering and Mathematics, University of Siena, Siena, Italy",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-15T15:13:59Z",
    "date_accepted": "2025-07-15T15:13:59Z",
    "date_published": "2025-07-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64986/galley/49796/download/"
        }
    ]
}