{
  "abstract": "The paper establishes a case of Howe duality for an exceptional theta correspondence using the ping-pong of types method. To that end, one needs to compute lifts of types of maximal compact subgroups. A brand new ingredient enters here: The graded module of the minimal representations is the coordinate ring of an affine cone whose projectivization is a Grassmannian. Via the filtered Nakayama lemma the problem of lifting types becomes a problem in algebraic geometry: compute certain linear sections of the Grassmannian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08716",
  "author_total": 1,
  "authors": [
    {
      "name": "Gordan Savin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bs67f891pwqgv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08716",
  "fulltext_url": null,
  "id": "bs67f891pwqgv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08716",
  "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.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08716",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bs67f891pwqgv.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08716",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08716"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Long-root $\\SL_2$ dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence",
  "title_text": "Long-root SL_2 dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/bs67f891pwqgv",
  "venue": "arXiv",
  "versions": []
}