{
  "abstract": "A bstract The emergence of the quantum R -matrix in the double-scaled SYK model points to an underlying quantum group structure. In this work, we identify the quantum group 𝒰 q (𝔰𝔲(1, 1)) as a subalgebra of the chord algebra. Specifically, we construct the generators of 𝒰 q (𝔰𝔲(1, 1)) from combinations of operators within the chord algebra and show that the one-particle chord Hilbert space decomposes into the positive discrete series representations of 𝒰 q (𝔰𝔲(1, 1)). Using the coproduct structure of the quantum group, we build the multi-particle Hilbert space and establish its equivalence with previous results defined by the chord rules. In particular, we show that the quantum R -matrix acts as a swapping operator that reverses the ordering of open chords in each fusion channel while incorporating the corresponding q -weighted penalty factors. This action enables an explicit derivation of the chord Yang-Baxter relation. We further explore a realization of the quantum group generators on the quantum disk, and present a novel factorization formula for the bulk gravitational wavefunction in the presence of matter. We also discuss the relation between the 𝒰 q (𝔰𝔲(1, 1)) structure uncovered here and the 𝒰 q (𝔰𝔩(2 , ℝ)) algebra previously studied from the boundary perspective. Finally, we study the gravitational wavefunction with matter in the Schwarzian regime.",
  "abstract_shown": true,
  "affiliations": [
    "University of British Columbia",
    "University of Amsterdam",
    "University of California"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jeremy van der Heijden",
      "orcid": "0000-0002-3708-6181"
    },
    {
      "affs": [
        1
      ],
      "name": "Erik Verlinde",
      "orcid": "0000-0002-9404-4009"
    },
    {
      "affs": [
        2
      ],
      "name": "Jiuci Xu",
      "orcid": "0009-0004-2544-9231"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4h878hytynwp.bib",
  "cited_by": 7,
  "doi": "10.1007/jhep05(2026)148",
  "fulltext_url": null,
  "id": "d4h878hytynwp",
  "issns": [
    "1029-8479",
    "1126-6708",
    "1127-2236"
  ],
  "landing_url": "https://doi.org/10.1007/jhep05(2026)148",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W4416379084",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/JHEP05(2026)148.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-13",
  "publisher": "Springer Nature",
  "ris": "https://research.draconitic.com/paper/d4h878hytynwp.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:02Z",
      "native_id": "W4416379084",
      "source": "openalex",
      "url": "https://doi.org/10.1007/jhep05(2026)148"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Quantum symmetry and geometry in double-scaled SYK",
  "title_text": "Quantum symmetry and geometry in double-scaled SYK",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T13:21:02Z",
  "url": "https://research.draconitic.com/paper/d4h878hytynwp",
  "venue": "Journal of High Energy Physics",
  "versions": []
}