{
  "abstract": "Let $\\mathcal{S}_χ$ be a cuspidal representation of $\\mathrm{GL}_2(q)$. A subset $S \\subseteq \\mathrm{GL}_2(q)$ is $t$-intersecting if $\\dim_{\\mathbb{C}}\\{v \\in \\mathcal{S}_χ: g_1v = g_2v\\} \\geqslant t$ for any $g_1, g_2 \\in S$. For $q = p^f$, where $p$ is an odd prime, $f \\geqslant 2$, and $1 \\leqslant t < p$ is an integer, we determine the maximum size of an $t$-intersecting subset when $χ(-1) = -1$, and when $χ(-1) = 1$ with $t \\leqslant 2$. The proof combines explicit fixed-space dimensions, attaining subgroup constructions, and weighted spectral bounds for normal Cayley graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38472",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiaqi Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjwdjchws2ztk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38472",
  "fulltext_url": null,
  "id": "cjwdjchws2ztk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38472",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38472",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjwdjchws2ztk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38472",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38472"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "EKR Results for Cuspidal Representations of $\\mathrm{GL}_2(q)$",
  "title_text": "EKR Results for Cuspidal Representations of GL_2(q)",
  "type": "preprint",
  "updated_at": "2026-11-05T15:21:00Z",
  "url": "https://research.draconitic.com/paper/cjwdjchws2ztk",
  "venue": "arXiv",
  "versions": []
}