{
  "abstract": "Let $\\hbar$ be a non-zero real number and put $q= e^{-πi \\hbar}$. Let $G$ be a semisimple split real Lie group of classical type, with Lie algebra $\\mathfrak{g}$ and associated Borel subalgebra $\\mathfrak{b} \\subseteq \\mathfrak{g}$. We show that there exists a locally compact quantum group $(L_{\\hbar}(B),Δ)$ which integrates the Borel part $U_q(\\mathfrak{b})$ of the Drinfeld--Jimbo quantized enveloping algebra $U_q(\\mathfrak{g})$, viewed as a Hopf $*$-algebra. We further compute the associated Haar weights and modular data for $(L_{\\hbar}(B),Δ)$. Up to an excess Cartan part, the Drinfeld double of $(L_{\\hbar}(B),Δ)$ can be seen as an analytic quantization of the function algebra of the totally positive semigroup $G^+\\subseteq G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13213",
  "author_total": 3,
  "authors": [
    {
      "name": "Kenny De Commer"
    },
    {
      "name": "Geoffrey Janssens"
    },
    {
      "name": "Wannes Malfait"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kpff8c6skaj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13213",
  "fulltext_url": null,
  "id": "1kpff8c6skaj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13213",
  "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.OA"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221573316",
  "pdf_url": "https://arxiv.org/pdf/2610.13213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kpff8c6skaj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Haar measure for totally positive split real semisimple quantum groups of classical type",
  "title_text": "Haar measure for totally positive split real semisimple quantum groups of classical type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/1kpff8c6skaj7",
  "venue": "arXiv",
  "versions": []
}