{
  "abstract": "We explore the quantum reflection equation in the case of a full-dimensional $n\\times n$ matrix $\\mathbb A$. Using the technique of $q$-determinants, we find closed expressions for the quantum Pfaffian (in the case of even $n$) and for new quantum Casimirs that are ratios of special quantum (Sklyanin) minors of $\\mathbb A$. Special attention is paid to the self-adjointness property of the newly constructed Casimirs. We put forward a conjecture that, adopting a natural ansatz for a quantum deformation of a Casimir of a classical algebra, self-adjointness implies commutativity. We also explore the relationship to networks of quantum cluster variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08796",
  "author_total": 3,
  "authors": [
    {
      "name": "Erik Brodsky"
    },
    {
      "name": "Leonid O Chekhov"
    },
    {
      "name": "Quanyu Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ensqbxqc2rdm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08796",
  "fulltext_url": null,
  "id": "4ensqbxqc2rdm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08796",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ensqbxqc2rdm.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:04Z",
      "native_id": "2611.08796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Constructing Casimirs for the quantum reflection equation",
  "title_text": "Constructing Casimirs for the quantum reflection equation",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/4ensqbxqc2rdm",
  "venue": "arXiv",
  "versions": []
}